You can put this solution on YOUR website! Notice that:
(x^2-1)
is a "difference of squares"
(x^2-1^2)
we can factor as:
(x-1)(x+1)
.
So, we can rewrite your original equation:
1/(x-1) + 1/2 = 2/(x^2-1)
as:
1/(x-1) + 1/2 = 2/[(x-1)(x+1)]
multiply both sides by 2:
2/(x-1) + 1 = 4/[(x-1)(x+1)]
Now, we multiply both sides by (x-1)(x+1) to get:
2(x+1) + (x-1)(x+1) = 4
2x+2 + x^2-1 = 4
x^2+2x-1 = 4
x^2+2x-5 = 0
applying "quadratic formula" to get
x = {1.45, -3.45}
.
