Question

How do you divide and simplify `\frac { x ^ { 2} - 4} { 4x - 4} \div \frac { x ^ { 2} + 4x + 4} { x ^ { 2} + x - 2}`?

Answer 1

`(x^2-4)/(4x-4)div(x^2+4x+4)/(x^2+x-2)=(x-2)/4`

Explanation:

`(x^2-4)/(4x-4)div(x^2+4x+4)/(x^2+x-2)`

`=(x^2-4)/(4x-4)*(x^2+x-2)/(x^2+4x+4)rarr` `a/cdivc/d=a/b*d/c`

`=((x)^2-(2)^2)/(4(x-1))*(x^2+2x-x-2)/(x^2+2x+2x+4)rarr`Factorise

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

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

`=((x+2)(x-2)(x+2)(x-1))/(4(x-1)((x+2)(x+2)`

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

`=(x-2)/4`