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

1 Answer
Aug 3, 2016

(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)