How do you solve #\frac { 7} { x - 3} - \frac { 6} { x + 1} = 1#?

1 Answer
Mar 18, 2017

x=7, -4

Explanation:

  1. Find the gcf of the fractions which is (x-3)(x+1)
    7(x+1) and 6(x-3)

  2. Subtract the two fractions.
    #(7x+7-(6x-18))/((x-3)(x+1))#

#(7x+7-6x+18)/((x-3)(x+1))# (Don't forget to distribute the negative)

#(x+25)/((x-3)(x+1))#

3.Multiply (x-3)(x+1) to get rid of the fractions.

x+25= (x-3)(x+1)
x+25= #x^2#-2x-3

  1. Bring all the terms to one side
    #x^2#-3x-28=0

5.Solve the equation (I'm assuming you know how to solve quadratic equations)

(x-7)(x+4)=0
x-7=0 x+4=0
x=7 x= -4

ANSWER: x=7, -4