Rational fractions MCQs With Answer

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Rational fractions MCQs With Answer are essential for B. Pharm students preparing for pharmaceutics, pharmaceutical analysis, and dosage calculations. This focused set covers rational expressions, simplification, partial fraction decomposition, improper versus proper fractions, and applications in drug formulation mathematics. Practicing targeted MCQs enhances conceptual clarity, calculation speed, and exam readiness. Each question includes clear answer choices to help identify common errors and strengthen problem-solving skills. These practice questions are tailored to pharmacy curricula and emphasize real-world examples relevant to drug stability, concentration ratios, and dilution problems. Regular practice of Rational fractions MCQs With Answer builds confidence for university exams and competitive tests. Now let’s test your knowledge with 50 MCQs on this topic.

Q1. Which expression is a proper rational fraction?

  • 7/(x+2)
  • (x^2 + 3x + 2)/(x – 1)
  • (2x^2 + 5x + 3)/(x + 1)
  • (x^3 + 1)/(x^2 + 2)

Correct Answer: 7/(x+2)

Q2. Identify the improper rational fraction.

  • (x + 4)/(x^2 + 1)
  • (3x^2 + 2)/(x + 1)
  • 5/(x^2 + 3)
  • 1/(x + 2)

Correct Answer: (3x^2 + 2)/(x + 1)

Q3. Simplify the rational fraction (x^2 – 1)/(x – 1).

  • x + 1
  • x – 1
  • 1
  • x^2 + x

Correct Answer: x + 1

Q4. Factor the denominator to prepare for partial fractions: 1/(x^2 – 5x + 6).

  • 1/[(x-2)(x-3)]
  • 1/[(x+2)(x+3)]
  • 1/(x^2 – 1)
  • 1/(x^2 + 5x + 6)

Correct Answer: 1/[(x-2)(x-3)]

Q5. Decompose into partial fractions: 3/(x(x+1)).

  • 3/x – 3/(x+1)
  • 2/x + 1/(x+1)
  • 1/x + 2/(x+1)
  • 3/x + 0/(x+1)

Correct Answer: 1/x + 2/(x+1)

Q6. For the rational expression (2x+3)/(x^2-1), the partial fraction form is:

  • A/(x-1) + B/(x+1)
  • A/(x^2-1)
  • A/(x-1) + Bx + C
  • A/x + B/(x^2-1)

Correct Answer: A/(x-1) + B/(x+1)

Q7. Which method often speeds up finding constants for simple linear factors?

  • Cover-up method
  • Long division
  • Completing the square
  • Matrix inversion

Correct Answer: Cover-up method

Q8. When is polynomial long division required before partial fractions?

  • When numerator degree ≥ denominator degree
  • When denominator has irreducible quadratic factors only
  • When numerator is zero
  • When denominator factors into distinct linear terms

Correct Answer: When numerator degree ≥ denominator degree

Q9. Simplify the complex fraction: ( (1/x) + (1/(x+1)) ) combined into a single rational expression.

  • (2x+1)/(x(x+1))
  • (2x+1)/(x+1)
  • (x+1)/(x)
  • (x+x+1)/(x(x+1))

Correct Answer: (2x+1)/(x(x+1))

Q10. Which of the following is a valid domain restriction for 1/(x^2-4)?

  • x ≠ 2 and x ≠ -2
  • x ≠ 4
  • x ≠ 0
  • No restriction

Correct Answer: x ≠ 2 and x ≠ -2

Q11. The sum of rational fractions 1/(x+1) + 1/(x+2) equals:

  • (2x+3)/[(x+1)(x+2)]
  • (x+3)/[(x+1)(x+2)]
  • (1)/(x+1)(x+2)
  • (x+1)/(x+2)

Correct Answer: (2x+3)/[(x+1)(x+2)]

Q12. Which expression is irreducible over the reals?

  • x^2 + 4
  • x^2 – 9
  • x^2 – 1
  • (x+2)(x-2)

Correct Answer: x^2 + 4

Q13. Partial fraction for (5x+6)/(x^2+3x+2) yields A/(x+1)+B/(x+2). Solve for A and B.

  • A=1, B=4
  • A=2, B=3
  • A=5, B=6
  • A=3, B=2

Correct Answer: A=1, B=4

Q14. For decomposition with repeated factor (1/(x-2)^2), the correct term includes:

  • A/(x-2) + B/(x-2)^2
  • A/(x-2)^2 only
  • A/(x-2) + Bx
  • A/(x-2) + B/(x+2)

Correct Answer: A/(x-2) + B/(x-2)^2

Q15. Evaluate partial fraction of (x+2)/(x(x+1)(x+2)). One term will be:

  • 1/(x)
  • 1/(x+2)
  • x/(x+1)
  • (x+2)/(x)

Correct Answer: 1/(x+2)

Q16. A rational function has a vertical asymptote where:

  • Denominator = 0 and numerator ≠ 0
  • Numerator = 0 exactly
  • Numerator and denominator equal
  • No factors cancel

Correct Answer: Denominator = 0 and numerator ≠ 0

Q17. After cancelling common factor (x-1) from (x^2-1)/(x-1), the original function had a:

  • Hole at x=1
  • Vertical asymptote at x=1
  • Horizontal asymptote at y=1
  • No discontinuity

Correct Answer: Hole at x=1

Q18. Which operation can convert an improper rational function into a proper one?

  • Polynomial long division
  • Factoring only
  • Cross-multiplication
  • Taking reciprocal

Correct Answer: Polynomial long division

Q19. The partial fraction of (4)/(x^2 – 1) can be written as:

  • 2/(x-1) – 2/(x+1)
  • 4/(x^2 – 1) only
  • 1/(x-1) + 3/(x+1)
  • 4/(x-1) + 0/(x+1)

Correct Answer: 2/(x-1) – 2/(x+1)

Q20. In pharmacy calculations, rational fractions often model:

  • Concentration dilution ratios
  • Sterilization temperature curves only
  • Tablet color
  • Brand preference

Correct Answer: Concentration dilution ratios

Q21. Solve for A and B: (6x+1)/(x^2-1) = A/(x-1) + B/(x+1).

  • A=3.5, B=2.5
  • A=3.5, B=-? (invalid)
  • A=3.5, B=2.5 is incorrect
  • A=3.5, B=2.5 (check with substitution)

Correct Answer: A=3.5, B=2.5

Q22. Which decomposition matches (x)/(x^2+1)?

  • Cannot be decomposed into real linear factors
  • A/(x+1) + B/(x-1)
  • A/(x^2+1)
  • A/(x) + B/(x^2+1)

Correct Answer: Cannot be decomposed into real linear factors

Q23. Combine into one rational expression: 1/(x) – 1/(x+2) equals:

  • 2/[(x)(x+2)]
  • 2x/[(x)(x+2)]
  • (x+2 – x)/[x(x+2)]
  • 0

Correct Answer: (x+2 – x)/[x(x+2)]

Q24. Which partial fraction approach is needed when denominator has irreducible quadratic factor?

  • Include linear numerator for that factor
  • Use only constants on numerator
  • Ignore that factor
  • Use exponential substitution

Correct Answer: Include linear numerator for that factor

Q25. For (x^2+1)/(x-1), perform polynomial division: quotient is:

  • x+1 with remainder 2
  • x-1 with remainder 2
  • x^2 with remainder 1
  • 1 with remainder x^2

Correct Answer: x+1 with remainder 2

Q26. A rational function with numerator and denominator degree equal has horizontal asymptote at:

  • Ratio of leading coefficients
  • y=0
  • y=1 always
  • No horizontal asymptote

Correct Answer: Ratio of leading coefficients

Q27. Which step is essential when simplifying rational fractions with polynomials?

  • Factor numerator and denominator completely
  • Differentiate numerator
  • Integrate denominator
  • Square both sides

Correct Answer: Factor numerator and denominator completely

Q28. Determine A and B: (7)/(x^2-4) = A/(x-2) + B/(x+2).

  • A=7/4, B=-7/4
  • A=7, B=0
  • A=3.5, B=3.5
  • A=0, B=7

Correct Answer: A=7/4, B=-7/4

Q29. The cover-up method cannot be applied when:

  • Factors are repeated
  • Factors are distinct linear
  • Denominator is quadratic irreducible
  • Numerator is constant

Correct Answer: Factors are repeated

Q30. Simplify: (x^2 – 4)/(x^2 – 5x + 6) after factoring.

  • (x+2)/(x-3)
  • (x-2)/(x-3)
  • (x+2)/(x+1)
  • (x-2)/(x+3)

Correct Answer: (x+2)/(x-3)

Q31. In drug dilution ratios, rational expressions help calculate:

  • Final concentration after mixing solutions
  • Pill color
  • Tablet hardness only
  • Marketing price

Correct Answer: Final concentration after mixing solutions

Q32. Which is the correct partial fraction for (8x+3)/(x^2+3x+2)?

  • 5/(x+1) + 3/(x+2)
  • 1/(x+1) + 7/(x+2)
  • 3/(x+1) + 5/(x+2)
  • 8/(x+1) + 3/(x+2)

Correct Answer: 3/(x+1) + 5/(x+2)

Q33. When decomposing (Ax+B)/(x^2+1), A and B correspond to:

  • Linear numerator over quadratic irreducible
  • Two separate constants over linear factors
  • Constants only for repeated linear factors
  • No decomposition possible

Correct Answer: Linear numerator over quadratic irreducible

Q34. Evaluate limit related to rational fractions: lim x→∞ (3x^2 + x)/(6x^2 – 2) equals:

  • 1/2
  • 0
  • 3/6 with remainder
  • Infinity

Correct Answer: 1/2

Q35. Cancel common factor and state resulting expression: (x(x-1))/(x^2 – x) becomes:

  • 1
  • x
  • Undefined due to cancellation but simplifies to 1
  • (x)/(x-1)

Correct Answer: Undefined due to cancellation but simplifies to 1

Q36. Which rational expression models mixing 100 mL of 10% solution with x mL of 2% solution for final concentration?

  • (100*10 + x*2)/(100+x)
  • 100/(10+x)
  • (10+x)/(100+x)
  • (100+x)/(10*2)

Correct Answer: (100*10 + x*2)/(100+x)

Q37. For decomposition with quadratic factor (x^2+1), general form includes:

  • (Ax+B)/(x^2+1)
  • A/(x^2+1) only
  • A/(x+1) + B/(x-1)
  • A/(x^2+1)^2

Correct Answer: (Ax+B)/(x^2+1)

Q38. Solve quickly: (x+1)/(x^2-1) = ? in partial fractions.

  • 1/2 * [1/(x-1) + 1/(x+1)]
  • 1/(x-1) – 1/(x+1)
  • 1/(x+1) only
  • x/(x-1)(x+1)

Correct Answer: 1/2 * [1/(x-1) + 1/(x+1)]

Q39. Which factorization is correct for x^3 – x?

  • x(x-1)(x+1)
  • (x-1)(x^2+1)
  • x^2(x-1)
  • (x+1)^3

Correct Answer: x(x-1)(x+1)

Q40. The degree of numerator of (2x^3 + x)/(x^2 + 1) is:

  • 3
  • 2
  • 1
  • 0

Correct Answer: 3

Q41. Convert improper to proper: (x^2 + 4x + 3)/(x + 1) gives quotient:

  • x + 3
  • x + 4
  • x^2 + 4
  • 1

Correct Answer: x + 3

Q42. For repeated linear factor decomposition of (2x+1)/(x-1)^2, the form includes:

  • A/(x-1) + B/(x-1)^2
  • A/(x-1)^2 only
  • A/(x-1) + B/(x+1)
  • A(x-1) + B

Correct Answer: A/(x-1) + B/(x-1)^2

Q43. Which rational expression simplifies to constant 2 when x ≠ 0?

  • (2x)/x
  • x/(2x)
  • (x+2)/(x+1)
  • (2x+1)/x

Correct Answer: (2x)/x

Q44. If partial fractions give A/(x-2) + B/(x-3), evaluating at x=2 gives:

  • A/(0) + B/( -1 ) so use cover-up to find A
  • Direct value of function
  • Value of B directly
  • No information

Correct Answer: A/(0) + B/( -1 ) so use cover-up to find A

Q45. Which rational expression has horizontal asymptote y=0?

  • 1/(x^3 + 1)
  • (x^2+1)/(x^2+2)
  • (2x^2)/(x^2+1)
  • (3x^2+1)/(x^2-1)

Correct Answer: 1/(x^3 + 1)

Q46. For fraction (x^2+2x)/(x^2-1), cancellation leads to simplified form when factoring numerator as x(x+2). Which is true?

  • No common factor with denominator
  • Cancels to (x+2)/(x-1)
  • Cancels to x/(x-1)
  • Cancels to 1

Correct Answer: No common factor with denominator

Q47. A rational equation solving might introduce extraneous solutions when:

  • Multiplying both sides by expressions that can be zero
  • Simplifying correctly
  • Factoring only
  • Adding like terms

Correct Answer: Multiplying both sides by expressions that can be zero

Q48. Which option best describes a complex fraction?

  • A fraction where numerator or denominator contains another fraction
  • A fraction with complex numbers
  • A fraction with exponents only
  • A simplified rational expression

Correct Answer: A fraction where numerator or denominator contains another fraction

Q49. For decomposition of (3x^2 + 2x +1)/(x(x^2+1)), one term will be:

  • A/x
  • B/(x+1)
  • C/(x-1)
  • D/(x+2)

Correct Answer: A/x

Q50. The practical benefit of mastering rational fractions for B. Pharm students is:

  • Improved accuracy in dosage and dilution calculations
  • Better knowledge of drug names
  • Enhanced ability to compound flavors
  • Faster pill packaging

Correct Answer: Improved accuracy in dosage and dilution calculations

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