How do you solve for x: #2/(x-3) - 3/(x+3) = 12/((x^2)-9) #?

1 Answer
Feb 25, 2017

#2/(x-3)-3/(x+3)=12/(x^2-9)#

#implies (2(x+3)-3(x-3))/((x+3)(x-3))=12/(x^2-9)#

#implies (2x+6-3x+9)/cancel(x^2-9)=12/cancel(x^2-9)#

#implies -x+15=12#

#implies x=3#

Verification: Put #x=3#

#L.H.S=2/(x-3)-3/(x+3)=2/(3-3)-3/(3+3)=2/0-3/6#

Here we can see #2/0#, in Mathematics, division by 0 is not allowed.
Hence, the root #x=3# is not a solution to the given equation.
Hence, no solution exists for the given equation.