How do you solve #4 / (x+1) + 3 /( x - 4) = 2 /( x +1)#?

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Answer 1 · 2018-03-22T16:11:01

#x# = #1#.

First, multiply and divide the first fraction on the left by #x-4# and the second fraction on the left by #x+1# to make them comparable.

We get #(4(x-4) + 3(x+1))/((x+1)(x-4))# = #2/(x+1)#.

After cancelling #x+1# on both sides, we get,

#(4(x-4) + 3(x+1))/(x-4)# = #2#.

On expanding the numerator and cross multiplying the denominator we get,

#7x-13# = #2x-8#

This gives us #5x# = #5#

And thus #x# = #1#.