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

1 Answer
Mar 19, 2016

Answer:

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!