How do you solve #5/(x+4) = 5/(3(x+1))#?

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Answer 1 · 2015-10-20T18:05:57

The solution is #x = 1/2#

In order to solve

#5/(x+4) = 5/(3(x+1))#

Begin by dividing both sides by 5.

#1/(x+4) = 1/(3(x+1))#

Then take the reciprocal of both sides:

#x+4 = 3(x+1)#

Expand the term on the right to be:

#x+4 = 3x+3#

Through some simple algebra you should be able to show that:

#1 = 2x#

#1/2 = x#

Checking the answer by substituting #1/2# for x, we can see that both sides will be equal:

#5/(1/2+4) = 5/(3(1/2+1))#

#5/(4.5) = 5/(3/2+3)#

#5/(4.5) = 5/(4.5)#