Question

How do you simplify `(x^2-3x+2)/(2x^2-2x)`?

Answer 1

See a solution process below:

Explanation:

We can factor the numerator and denominator as;

`((x - 2)(x - 1))/(2x(x - 1))`

We can now cancel common term in the numerator and denominator:

`((x - 2)cancel((x - 1)))/(2xcancel((x - 1))) =>`

`(x - 2)/(2x)`

However, we cannot divide by `0` so we must exclude:

`2x = 0 => x = 0` and `x - 1 = 0 => x 1`

`(x^2 - 3x + 2)/(2x^2 - 2x) = (x - 2)/(2x)` Where: `x != 0` and `x != 1`

Or

`(x^2 - 3x + 2)/(2x^2 - 2x) = x/(2x) - 2/(2x) = 1/2 - 1/x` Where: `x != 0` and `x != 1`