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}
.
| Solved by pluggable solver: SOLVE quadratic equation with variable |
Quadratic equation  (in our case  ) has the following solutons:
For these solutions to exist, the discriminant  should not be a negative number.
First, we need to compute the discriminant :  .
Discriminant d=24 is greater than zero. That means that there are two solutions:  .
Quadratic expression  can be factored:
Again, the answer is: 1.44948974278318, -3.44948974278318.
Here's your graph:
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