Question

How do you find the quotient of `(5x^2)/(x^2-5x+4)div(10x)/(x-1)`?

Answer 1

See a solution process below:

Explanation:

First, factor the denominator of the fraction on the left:

`(5x^2)/(x^2 - 5x + 4) -: (10x)/(x - 1) => (5x^2)/((x - 4)(x - 1)) -: (10x)/(x - 1)`

Next, rewrite this expression as:

`((5x^2)/((x - 4)(x - 1)))/((10x)/(x - 1))`

Then, use this rule of dividing fractions to rewrite the expression again and find the quotient:

`(color(red)((5x^2))/color(blue)(((x - 4)(x - 1))))/(color(green)((10x))/color(purple)((x - 1))) => (color(red)((5x^2)) xx color(purple)((x - 1)))/(color(blue)(((x - 4)(x - 1))) xx color(green)((10x)))`

`(color(red)((cancel(5)cancel(x^2)x)) xx cancel(color(purple)((x - 1))))/(color(blue)(((x - 4)cancel((x - 1)))) xx color(green)((cancel(10)2cancel(x)))) =>`

`x/(2(x - 4))` or `x/(2x - 8)`