Question

How do you simplify `\frac { 2x } { x ^ { 2} + 8x - 9} \div ( \frac { x ^ { 2} + 4x } { x ^ { 2} - 81} \cdot \frac { x - 9} { x + 4} )`?

Answer 1

`(2x)/(x^2+8x-9) div ((x^2+4x)/(x^2-81)*(x-9)/(x+4))=2/(x-1)`

Explanation:

This question is best done by factorising expressions wherever you can, and then going on from there.

`(2x)/(x^2+8x-9) div ((x^2+4x)/(x^2-81)*(x-9)/(x+4))`

`=(2x)/((x-1)(x+9)) div ((x(x+4))/((x-9)(x+9))*(x-9)/(x+4))`

Following BODMAS, we work with what's in the brackets first.

`=(2x)/((x-1)(x+9)) div ((x(cancel(x+4)))/((cancel(x-9))(x+9))*cancel(x-9)/cancel(x+4))`

`=(2x)/((x-1)(x+9)) div (x/(x+9))`

We can change this division sign into a multiplication sign by flipping the fraction on the right.

`=(2(cancel(x)))/((x-1)(cancel(x+9))) xx cancel(x+9)/cancel(x)`

`=2/(x-1)`

So, `(2x)/(x^2+8x-9) div ((x^2+4x)/(x^2-81)*(x-9)/(x+4))=2/(x-1)`