Question

How do you divide and simplify `(frac { 6x ^ { 2} + x - 2} { 4x ^ { 3} - 16x ^ { 2} - x + 4} ) \div ( \frac { 9x ^ { 2} + 12x + 4} { 6x ^ { 2} + 7x + 2} )`?

Answer 1

`color(magenta)((3x+1)/((x-4)(2x+1))`

Explanation:

`(6x^2+x-2)/(4x^3-16x^2-x+4)-:(9x^2+12x+4)/(6x^2+7x+2)`

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

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

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

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

`:.color(magenta)(=((3x+1))/((x-4)(2x+1))`