Question

How do you simplify `(x^2-x-12)/(8x^2)div(x^3+3x^2)/(8x^3-2x^2)div(4x-1)/(x+2)`?

Answer 1

`(x^2-x-12)/(8x^2)-:(x^3+3x^2)/(8x^3-2x^2)-:(4x-1)/(x+2)=((x-4)(x+2))/(4x^2)`

Explanation:

`(x^2-x-12)/(8x^2)-:(x^3+3x^2)/(8x^3-2x^2)-:(4x-1)/(x+2)`

= `(x^2-4x+3x-12)/(8x^2)-:(x^2(x+3))/(2x^2(4x-1))-:(4x-1)/(x+2)`

= `(x(x-4)x+3(x-4))/(8x^2)-:(x^2(x+3))/(2x^2(4x-1))-:(4x-1)/(x+2)`

= `((x+3)(x-4))/(8x^2)xx(2x^2(4x-1))/(x^2(x+3))xx(x+2)/(4x-1)`

= `(cancel((x+3))(x-4))/(4cancel(8x^2))xx(cancel((2x^2))cancel((4x-1)))/(x^2cancel((x+3)))xx(x+2)/(cancel((4x-1))`

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