How do you solve 12/(a+3)+6/(a^2-9)=8/(a+3)?

1 Answer
Mar 27, 2018

color(blue)(x=3/2)

Explanation:

12/(a+3)+6/(a^2-9)=8/(a+3)

factor (a^2-9)

This is the difference of two squares:

(a^2-b^2)=(a+b)(a-b)

(a^2-3^2)=(a+3)(a-3)

12/(a+3)+6/((a+3)(a-3))=8/(a+3)

Multiply through by (x+3)

(a+3)12/(a+3)+(a+3)6/((a+3)(a-3))=(a+3)8/(a+3)

Cancel:

cancel((a+3))12/cancel((a+3))+cancel((a+3))6/(cancel((a+3))(a-3))=cancel((a+3))8/cancel((a+3))

12+6/(x-3)=8

Subtract 12

6/(x-3)=-4

Multiply by (x-3)

(x-3)6/(x-3)=-4(x-3)

Cancel:

cancel((x-3))6/(cancel(x-3))=-4(x-3)

6=-4(x-3)

Divide by -4

x-3=6/-4

x=6/-4+3=3/2

color(blue)(x=3/2)