How do you combine #(4a-2)/(3a+12)-(a-2)/(a+4)#?

2 Answers
Jan 8, 2018

See a solution process below:

Explanation:

To subtract or add fractions they must be over a common denominator. We can multiply the fraction on the right by the appropriate form of #1# to put these fractions over a common denominator:

#(4a - 2)/(3a + 12) - (3/3 xx (a - 2)/(a + 4)) =>#

#(4a - 2)/(3a + 12) - (3(a - 2))/(3(a + 4)) =>#

#(4a - 2)/(3a + 12) - (3a - 6)/(3a + 12)#

We can now subtract the numerators over the common denominator:

#((4a - 2) - (3a - 6))/(3a + 12) =>#

#(4a - 2 - 3a + 6)/(3a + 12) =>#

#(4a - 3a - 2 + 6)/(3a + 12) =>#

#((4 - 3)a + (-2 + 6))/(3a + 12) =>#

#(1a + 4)/(3a + 12) =>#

#(a + 4)/(3a + 12)#

We can now factor the numerator and cancel common terms:

#(a + 4)/(3(a + 4)) =>#

#color(red)(cancel(color(black)(a + 4)))/(3color(red)(cancel(color(black)((a + 4))))) =>#

#1/3#

Jan 8, 2018

This equals #1/3#, with restriction #a != -4#

Explanation:

We can factor the denominator of the left-most expression as #3(a + 4)#, thus we multiply the second fraction by #3#.

#=(4a - 2 - 3(a - 2))/(3a + 12)#

#=(4a - 2 - 3a + 6)/(3a + 12)#

#=(a + 4)/(3a + 12)#

#=(a + 4)/(3(a + 4))#

#=1/3#

But don't forget that #a != -4#.

Hopefully this helps!