In solving rational equations, what's the answer to... 1/(x-1)+3/(x+1)=2 and how do you find it? Thanks :)

Question

I don't have a very good calculator and I have a test tomorrow. Questions like this will be on the test; and I would like to know the steps in solving it. It would help me understand how to do it.

Answer 1

1/(x-1)+3/(x+1)=2
LCD of fractions = (x - 1)(x + 1)
Multiply both sides by LCD
1(x + 1) + 3(x - 1) = 2(x - 1)(x + 1)
x + 1 + 3x - 3 = 2(x² - 1)
4x - 2 = 2x² - 2
2x² - 4x = 0
2x(x - 2) = 0
x = 0 or 2

Check:
x = 0
1/(x-1)+3/(x+1) = 1/-1 + 3/1 = 2 Yesssssssssssssssssssssss!!

x = 2
1/(x-1)+3/(x+1) = 1/1 + 3/3 = 2 Yesssssssssssssssssssssss!!

Answer 2

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

Multiply everything by (x - 1)(x + 1)

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

Divide both sides by 2(x - 1)

1 = x + 1
x = 0

ANS : x = 0

if you go to www.quickmath.com, click on solve under Equations, type it in like i did, and you will get x = 0. It will also give you x = 2

Answer 3

x=2 here is explaination 1/x-1+3/x+1=2 x+1+3x-3/(x-1)(x+1)=2 x+1+3x-3=4x-2 so 4x-2=2(x-1)(x+1) 2(2x-1)=2(x-1)(x+1) 2 from left through 2 from right(2/2) =1 it disapeared 2x-1=(x-1)(x+1) and (x-1)(x+1)=x^2-1^2=x^2-1 so 2x-1=x^2-1 2x=x^2-1+1 2x=x^2 so 2=x^2/x=x finished 2=x or x=2 it s all l think u ll understand

Answer 4

use a calculator to find out