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

Question

Kennedy Adams · Accepted Answer

#x=0#, #x=2# #1/(x-1)+3/(x+1)=2# #rArr ((x+1)+3(x-1))/((x-1)(x+1))=2# #rArr (x+1+3x-3)/((x-1)(x+1))=2# #rArr (4x-2)/((x-1)(x+1))=2# #rArr 4x-2=2(x+1)(x-1)# #rArr 4x-2=2x+2(x-1)# #rArr 4x-2=2x^2-2x+2x-2# #rArr 4x-2=2x^2-2# #rArr 2x^2-4x=0# #rArr 2x(x-2)=0# #rArr x-2=0 -> x=2# #rArr 2x=0 -> x=0#

Avery Alexander · Answer

#x_1=0# and #x_2=2# #1/(x-1)+3/(x+1)=2# #[1*(x+1)+3*(x-1)]/[(x-1)(x+1)]=2# #(4x-2)/(x^2-1)=2# #4x-2=2*(x^2-1)# #x^2-1=2x-1# #x^2-2x=0# #x*(x-2)=0# Hence #x_1=0# and #x_2=2#

Savannah Anderson · Answer

undefined To solve the equation 1/(x-1) + 3/(x+1) = 2, you can follow these steps:

1. Find a common denominator for the fractions on the left side of the equation. In this case, the common denominator is (x-1)(x+1).

2. Multiply each term by the common denominator to eliminate the fractions. This gives you (x+1) + 3(x-1) = 2(x-1)(x+1).

3. Simplify the equation by distributing and combining like terms. This results in x + 1 + 3x - 3 = 2(x^2 - 1).

4. Continue simplifying the equation by combining like terms. This gives you 4x - 2 = 2x^2 - 2.

5. Rearrange the equation to bring all terms to one side, resulting in 2x^2 - 4x = 0.

6. Factor out the common factor of 2x, giving you 2x(x - 2) = 0.

7. Set each factor equal to zero and solve for x. This gives you two possible solutions: x = 0 and x = 2.

Therefore, the solutions to the equation 1/(x-1) + 3/(x+1) = 2 are x = 0 and x = 2.