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

Answer:

#(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)#