Question

Can you simplify `\frac { 2z ^ { 2} + 6} { z ^ { 2} - 2z - 24}`?

Answer 1

`frac(2 z^(2) + 6)((z + 4)(z - 6))`; `z ne - 4, 6`

Explanation:

We have: `frac(2 z^(2) + 6)(z^(2) - 2 z - 24)`

Let's factorise the denominator using the "middle-term break":

`= frac(2 z^(2) + 6)(z^(2) + 4 z - 6 z - 24)`

`= frac(2 z^(2) + 6)(z (z+ 4) - 6 (z + 4))`

`= frac(2 z^(2) + 6)((z + 4)(z - 6))`; `z ne - 4, 6`