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#