Question 464266
To solve the equation {{{1/(x-1)+4/(x^2-1)=(-2)/(x^2-2x+1)}}}, first we factor the 

denominators to find the LCD.{{{1/(x-1)+4/(x-1)(x+1)=(-2)/(x-1)^2}}}. the LCD is

{{{(x-1)^2(x+1)}}}. Second write all terms with the same denominator:

{{{(x-1)(x+1)/(x-1)^2(x+1)+4(x-1)/(x-1)^2(x+1)=-2(x+1)/(x-1)^2(x+1)}}}

Multiply both sides by LCD, and cancel like terms:

{{{x^2-1+4(x-1)=-2(x+1)}}}, set the equation equal to zero:{{{x^2-2x-3=0}}}

Solve this equation by factoring:{{{(x+1)(x-3)=0}}} The solution is:

x+1=0 <=> x=-1, and x-3=0 <=> x=3. Reject the solution x=-1 because the equation is undefined and the only solution is x=3.