Question

Solve the equation or Inequality
x/(x^2-1) + 2/(x+1)=1+ 1/(2x-2)

Answer 1

\[\frac{x}{x^2-1}+\frac{2}{x+1}=1+\frac{1}{2x-2}\]

Answer 2

yes and thanks btw again

Answer 3

yw

Answer 4

Did you get it , its just the same question you posted

Answer 5

the least common multiple method will work here as well
or you can just grind it out
the least common multiple in this case is \(2(x^2-1)\)

Answer 6

\[2(x^2-1)\left(\frac{x}{x^2-1}+\frac{2}{x+1}\right)=2(x^2-1)\left(1+\frac{1}{2x-2}\right)\] is a start

Answer 7

Maybe you could also cross-multiply , both methods would work

Answer 8

multiply out cancelling as you go, gives
\[2x+2\times 2(x-1)=2x^2-2+x+1\]

Answer 9

\[2x+4x-4=2x^2+x-1\] and you can solve that quadratic

Answer 10

how is the least common multiple 2(x^2-1)

Answer 11

because \(x^2-1)=(x+1)(x-1)\) and \(2x-2=2(x-1)\)

Answer 12

but how does that work for x+1?

Answer 13

so the factors are
\[(x-1)(x+1), x+1,2(x-1)\] and the least common multiple is therefore
\[2(x+1)(x-1)\]

Answer 14

oh

Answer 15

but dont you have to have 1/1?