Question

How do you simplify `\frac { 5x ^ { 2} - 35x } { 7x ^ { 2} - 49x }`?

Answer 1

See the entire solution process below:

Explanation:

First, factor a `5x` out of the numerator and factor a `7x` out of the denominator:

`((5x * x) - (5x * 7))/((7x * x) - (7x * 7)) ->`

`(5x(x - 7))/(7x(x - 7))`

Next, cancel the common terms in the numerator and denominator:

`(5color(blue)(cancel(color(black)(x)))color(red)(cancel(color(black)((x - 7)))))/(7color(blue)(cancel(color(black)(x)))color(red)(cancel(color(black)((x - 7))))) ->`

`5/7`

However, we must keep the integrity of the original problem and ensure we do not divide by `0`.

Therefore the answer is `5/7` where `x != 0` and `x != 7`