Question 526735
{{{1/(x-1)^2+3/(x^2-1)=(5)/(x^2-1))}}}
{{{1/(x-1)^2+3/(x-1)(x+1)=(5)/(x-1)(x+1))}}}
{{{1/(x-1)^2+3/(x-1)(x+1)-5/(x-1)(x+1)=0)}}}
Taking LCD
{{{(1(x+1)+3(x-1)-5(x-1))/(x-1)^2(x+1)=0)}}}
{{{(x+1+3x-3-5x+5)/(x-1)^2(x+1)=0)}}}
{{{(x+3x-5x+1-3+5)/(x-1)^2(x+1)=0)}}}
{{{(-x+3)/(x-1)^2(x+1)=0)}}}
{{{(3-x)/(x-1)^2(x+1)=0)}}}
Multiply by {{{(x-1)^2(x+1)}}} both sides
{{{(x-1)^2(x+1)((3-x)/(x-1)^2(x+1))=(x-1)^2(x+1)*0)}}}
{{{cross((x-1)^2(x+1))((3-x)/cross((x-1)^2(x+1)))=0)}}}
{{{3-x=0)}}}
{{{3=x)}}}
{{{x=3)}}}



Check
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{{{1/(3-1)^2+3/((3)^2-1)=(5)/((3)^2-1))}}}
{{{1/(2)^2+3/((3)^2-1)=(5)/((3)^2-1))}}}
{{{(1/4)+(3/(9-1))=(5)/((9-1))}}}
{{{(1/4)+(3/8)=5/8)}}}
Take LCD
{{{((1*2)+3)/8)=5/8)}}}
{{{(2+3)/8=5/8)}}}
{{{5/8=5/8)}}}