How do you subtract and simplify \frac { x - 5} { 2x - 6} - \frac { x - 7} { 4x - 12} x52x6x74x12?

1 Answer
May 22, 2017

The expression simplifies to 1/414

Explanation:

Factor the denominators of each fraction

(x-5)/(2(x-3))-(x-7)/(4(x-3))x52(x3)x74(x3)

Find a common denominator.
Multiply the numerator and denominator of first fraction
by 22

(2(x-5))/(4(x-3))-(x-7)/(4(x-3))2(x5)4(x3)x74(x3)

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

(2(x-5)-(x-7))/(4(x-3))2(x5)(x7)4(x3)

Distribute the 22 and the negative sign in the numerator.

(2x-10-x+7)/(4(x-3)2x10x+74(x3)

Combine like terms in the numerator.

(x-3)/(4(x-3))x34(x3)

The (x-3)(x3) in the numerator and denominator cancel out
leaving you with 1/414