How do you simplify #\frac { 1} { u - 4} + \frac { 6} { u ^ { 2} - 16} = \frac { 3} { u + 4}#?

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Answer 1 · 2017-08-12T17:16:06

Because #(u-4)(u+4)=u^2-16#, one can eliminate all of the denominators by multiplying by #(u-4)(u+4)# and then solve for u.

Given: #\frac { 1} { u - 4} + \frac { 6} { u ^ { 2} - 16} = \frac { 3} { u + 4}#

Multiply both sides by #(u-4)(u+4)#:

#u+ 4 + 6 = 3(u-4)#

Solve for u:

#u+10 = 3u-12#

#-2u = -22#

#u = 11 larr# This is simplified

Check:

1/(11-4)+6/(11^2-16)=3/(11+4)

#1/7+ 6/105=3/15#

#1/7+ 2/35 = 1/5#

#5/35+2/35 = 7/35#

This checks.