Your not wrong when you say this is hard...
I'll take a shot at it...
I got the values x = 2
and x = -1
They seem to work...
I first factored 4x^2 - 1 to get (2x + 1)(2x - 1). When we add fractions we multiply the denominators to get the common denominator.
When I factored 4x^2 - 1 I got (2x + 1)(2x - 1) and that is the same denominator when you multiply the other 2 denominators together.
We get 4x/(2x + 1)(2x - 1)
We multiply 1 by (2x + 1)(2x - 1) so the denominator cancels out.
We get 4x + 7 = (2x + 1)(2x - 1)
We expand (2x + 1)(2x - 1) to get 4x^2 - 1.
4x + 7 = 4x^2 - 1
We subract 7 on both sides to receive 4x^2 - 8 = 4x
Then, we subtract 4x from both sides to get 4x^2 - 8 - 4x = 0
We can use the quadratic formula to find the solution from here on out.
a = 4, b = -4, c = -8
\(x = {-4 + \sqrt{(-4)^2-4(4(-8)} \over 2(4)}\)
Saving you time, this gives us 2 and -1.