GB-40-03-001 · Adding algebraic fractions

Write as a single fraction $\frac{7}{x+9}+\frac{8}{x-5}$ , where x ≠ −9, 5.

Algebraic Fractions: Addition / Subtraction Booklet p. 8 & p. 9

Method

1) Cross multiply (including denominators!)

2) Write as one fraction

3) Expand and simplify numerator

Worked Example (GB-40-03-001)

Booklet p. 8–9: Cross-multiply (

\mathbf{\times}

) including the denominators!

1) Use denominator

(x+9)(x-5)

7(x-5)+8(x+9)

\frac{15x + 37}{(x+9)(x-5)}

\frac{15x + 37}{(x+9)(x-5)}