Question

How do you solve `12/(v^2-16) - 24/(v-4) = 3`?

Answer 1

You have to put on an equal denominator.

Explanation:

First, factor the denominator to find the LCD (Least Common Denominator).

`12/((v -4)(v + 4)) - 24/(v - 4) = 3`

The LCD is `(v - 4)(v + 4)`

`12/((v - 4)(v + 4)) - (24(v + 4))/((v - 4)(v + 4)) = (3(v - 4)(v + 4))/((v - 4)(v + 4))`

We can now eliminate the denominator since all the fractions are now equivalent.

`12 - 24v + 96 = 3(v^2 - 16)`

`12 - 24v + 96 = 3v^2 - 48`

`0 = 3v^2 + 24v - 156`

`0 = 3(v^2 + 8v - 52)`

Solving by completing the square since factoring isn't possible:

`0 + 52= 1(v^2 + 8v + 16 - 16)`

`52 = (v + 4)^2`

`+-sqrt(52) = v + 4`

`+-sqrt(52) - 4 = v`

`+-2sqrt(13) - 4 = v`

Hopefully this helps!