Sam, this is the solution:
x/x+4 = 20/(x^2+3x-4) + 2/x-1
Step 1: Let's factor x^2+3x-4, this way:
x^2+3x-4 = (x +4) (x - 1)
Then we have:
x/x+4 = 20/(x + 4)(x -1) + 2/x-1
Step 2: Let's find the Lowest common denominator:
We have:
(x + 4), (x + 4)(x -1), (x - 1)
Lowest common denominator = (x + 4) (x - 1)
Step 3:Now we can divide (x + 4) (x - 1) by each denominator and multiply by the numerator, as follows:
x (x - 1) = 20 + 2(x + 4)
x² - x = 20 + 2x + 8
Step 4: Like terms
x² - x -2x = 28
x² - 3x - 28 = 0
Step 5: Let's factor again
(x - 7) (x + 4) = 0
Step 6: Find the solutions for x
x - 7 = 0
x1 = 7
x + 4 = 0
x = -4
x2 = -4
Sam, the equation has two solutions: (-4, 7)