Question 80158
{{{q^2/(q^2-16)-2/(q-4) = 3/(q+4)}}}
First, factor that denominator to make it easier to see what the upcoming LCD needs to be for combining this mess:
{{{q^2/((q+4)(q-4))-2/(q-4) = 3/(q+4)}}}
Get all like terms on one side of the equation:
{{{q^2/((q+4)(q-4))-2/(q-4)-3/(q+4)=0}}}
Now, you can see that the LCD is (q+4)(q-4). You can rewrite the equation in terms of this LCD:
{{{q^2/((q+4)(q-4))-(2(q+4))/((q+4)(q-4))-(3(q-4))/((q+4)(q-4))=0}}}
Now, combine all like terms. You should get:
{{{(q^2-2q-8-3q+12)/((q+4)(q-4))=0}}}
Simplifying...
{{{(q^2-5q+4)/((q+4)(q-4))=0}}}
Now, factor that numeraotr so you can have a cancelling opportunity:
{{{(q-1)(q-4)/((q+4)(q-4))=0}}}
Aha, you can cancel the (q-4) terms.
{{{((q-1)/(q+4))=0}}}
{{{highlight(q=1)}}}