Question

How do you subtract and simplify `\frac { x - 5} { 2x - 6} - \frac { x - 7} { 4x - 12}`?

Answer 1

The expression simplifies to `1/4`

Explanation:

Factor the denominators of each fraction

`(x-5)/(2(x-3))-(x-7)/(4(x-3))`

Find a common denominator.
Multiply the numerator and denominator of first fraction
by `2`

`(2(x-5))/(4(x-3))-(x-7)/(4(x-3))`

Since we now have a common denominator we can
rewrite as one fraction.

`(2(x-5)-(x-7))/(4(x-3))`

Distribute the `2` and the negative sign in the numerator.

`(2x-10-x+7)/(4(x-3)`

Combine like terms in the numerator.

`(x-3)/(4(x-3))`

The `(x-3)` in the numerator and denominator cancel out
leaving you with `1/4`