Precalc problem- finding all real solutions

Question

Can someone help me solve this precalc problem? I'd really appreciate it!

 

Find all real solutions of the equation. (Enter your answers as a comma-separated list. If there is no real solution, enter NO REAL SOLUTION.)

 

    1    +   1      =  5
x − 1     x + 2       4

Edit: The formatting turned out a bit strange, those spaces should have division symbols. So the problem is (1÷x-1) + (1÷x+2) = (5÷4)

Answer 1

Multiply both sides by (x-1)(x+2)

When you do this, I believe you will get 5x² - 3x - 14 = 0

You can either try to factor, or solve using the quadratic equation.

Answer 2

1/(x-1)+1(x+2)=5/4 (multiply both sides by 4(x-1)(x+2)

4(x+2+x-1)=5(x-1)(x+2)

8x+4=5x²+5x-10

5x²-3x-14=0.

If you solve this equation, you get x=-7/5 and x=2.