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

1 Answer
Oct 3, 2016

Answer:

#x=1#

Explanation:

The usual approach might be to multiply by the LCD to cancel the denominators. However two of the denominators are the same.
Put them together on one side.

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

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

#(2)/(x+1) = 3/-(x-4)" "larr# one fraction each side, cross-multiply

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

#3x+3 =-2x+8#

#3x+2x = 8-3#

#5x = 5#

#x =1#