How do you solve the rational equation 1/(x-1)+3/(x+1)=21x−1+3x+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= 1x−1=0⇔x=1
x+1 = 0 <=> x = -2 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)(x−1)(x+1)(1x−1)+(x−1)(x+1)(3x+1)=2(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