Algebraic Fractions — O/L Mathematics

What must I remember about Algebraic Fractions?

• An algebraic fraction is a rational expression P(x) / Q(x), where P and Q are polynomials and Q(x) ≠ 0.
• Simplifying algebraic fractions: Completely factorise numerator and denominator; cancel only common multiplicative factors, never individual terms.
• Addition and subtraction: Find the LCM of the algebraic denominators, express each fraction with the common denominator, and combine numerators.
• Multiplication: Multiply numerators together and denominators together after cancelling common factors: (P/Q) × (R/S) = (PR / QS).
• Division: Multiply by the reciprocal of the divisor fraction: (P/Q) ÷ (R/S) = (P/Q) × (S/R).

Test yourself (1 minute)

1. The illegal cancellation blunder

   In (x + 2) / (x + 5), NEVER cancel the x's; terms separated by + or - cannot be cancelled individually.

2. Sign change trap in subtraction

   In (a/b) - ((c - d)/e), the negative sign applies to the ENTIRE numerator: - (c - d) = -c + d.

3. Restricted denominator values

   Algebraic fractions are undefined when the denominator equals zero (e.g., 3 / (x - 2) is undefined when x = 2).

Practise Algebraic Fractions questions today

Source: NIE G.C.E. (O/L) Mathematics Syllabus (Grade 10, Unit 12)

What should I study first?

What comes next?

Next in the syllabus

Where does Algebraic Fractions fit in the syllabus?

Grade 10 · Term 2 · Grade 11 · Term 1