Question

How do you simplify `(x^2+x-6)/(2x^2)*(2x+8)/(x^2+7x+12)`?

Answer 1

`(x-2)/x^2`

Explanation:

`[x^2+(3-2)x-6]/(2x^2)*[2(x+4)]/[x^2+(3+4)x+12]`

`rArr [x^2+3x-2x-6]/[(cancel 2)x^2]*[(cancel 2)(x+4)]/[x^2+3x+4x+12]`

`rArr{x(x+3)-2(x+3)}/x^2*(x+4)/[x(x+3)+4(x+3)]`

`rArr[(x+3)(x-2)]/x^2*(x+4)/[(x+3)(x+4)]`

`rArr[(x-2){cancel(x+3)cancel(x+4)}]/[x^2{cancel(x+3)cancel(x+4)}]`

`rArr (x-2)/x^2`