GB-40-01-001 · Cancelling algebraic factors

Simplify $\frac{7x+63}{x^2-81}$ , where x ≠ ±9.

Algebraic Fractions: Simplifying (Linear & DOTS) Booklet p. 6 & p. 7

Method

1) Factorise numerator (take out HCF) and denominator (using DOTS a² − b² = (a − b)(a + b))

2) Cancel common bracket

Worked Example (GB-40-01-001)

1) Factorise numerator (HCF Grid, p. 4) & denominator (DOTS, p. 6):

Booklet p. 4 — Factorising Grid (HCF outside left, fill in top brackets):

×	$x$	$+9$
$7$	$7x$	$+63$

• HCF of

7

and

63

\mathbf{7}

• Factor out

\mathbf{7}

outside the grid

• Outside factor

= \mathbf{7}

Denominator (DOTS):

x^2 - 81 = (x - 9)(x + 9)

2) Cancel common bracket

(x + 9)

\quad \frac{7\cancel{(x + 9)}}{(x - 9)\cancel{(x + 9)}} = \mathbf{\frac{7}{x - 9}}

\frac{7}{x-9}