Question

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

Answer 1

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