GB-40-04-001 · Multiplying algebraic fractions

Simplify $\frac{x^2-225}{7x}\times\frac{7}{x+15}$ , where x ≠ 0, −15.

Algebraic Fractions: Multiplying / Dividing Booklet p. 8

Method

1) Factorise numerators and denominators (using DOTS)

2) Cancel common factors in numerator & denominator

Worked Example (GB-40-04-001)

1) Booklet p. 6 & p. 8 — Factorise

x^2 - 225

using DOTS:

(x - 15)(x + 15)

2) Cancel common factors in numerator & denominator:

\frac{(x - 15)\cancel{(x + 15)}}{\cancel{7}x} \times \frac{\cancel{7}}{\cancel{(x + 15)}} = \frac{x - 15}{x}

\frac{x-15}{x}