How do you solve #\frac { 1} { x - 2} + \frac { 3} { x + 3} = \frac { 4} { x ^ { 2} + x - 6}#?

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Answer 1 · 2018-03-07T18:46:16

#x=7/4 = 1 3/4#

First, let's work on the left hand side to put the terms over a common denominator:

#(x+3)/(x+3) * 1/(x-2)+ (x-2)/(x-2) * 3/(x+3) = (4x-3)/(x^2+x-6)#

Now we can set this equal to the right hand side:

#(4x-3)/(x^2+x-6)=4/(x^2+x-6)#

knowing the denominator is the same we can set the numerators equal to each other:

#4x-3=4#

#x=7/4 = 1 3/4#