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

1 Answer
May 22, 2017

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