Algebra 10

4 marks · Hard

Express the following as a single simplified fraction:

Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.

Show answer

\frac{x^2 + 7x - 12}{(x-4)(x+4)}

Also accept: \frac{(x+3)(x+4) + 2x}{(x-4)(x+4)} = \frac{x^2 + 7x - 12}{(x-4)(x+4)}

Common mistakes: Using x^2-16+x-4 in denominator instead of product

Show mark scheme and worked solution

Marking points

M1 · 1 mark · Correctly factorises the quadratic denominator as (x-4)(x+4).

M2 · 1 mark · Finds a correct common denominator and rewrites both fractions with it.

M3 · 1 mark · Correctly expands and combines the numerators with clear working. (follow-through)

A1 · 1 mark · Writes the final answer as a single simplified fraction (accept numerator as expanded or factorised form but must be fully simplified). (follow-through)

Worked solution

First, factorise the denominator of the second fraction:

So:

Add the fractions:

Expand the numerator:

But correct is:

Wait, let's verify.

So the final answer is: