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

##### 1 Answer

#### Explanation:

**Step 1** : Identify the restricted value.

This is done by set the denominator equal to zero like this

# x-1= 0 <=> x= 1#

#x+1 = 0 <=> x = -2 # The idea of restricted value, is to narrow down what value our variable can't be (aka domain)

Step 2: Multiply the equation by

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

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

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

**Step 3:** Multiply and combine like terms

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

#4x -2 = 2(x^2 -1)#

#4x -2 = 2x^2 -2#

#0 =2x^2-4x#

**Step 4:** Solve the quadratic equation

**Step 5** Check your solution ..

Check to see if the answer from Step 4 is the same a restricted value.

If it's not, the the solution is