Solve for x 1/x + -1/x+1 = 1/20?

Question

1/x + -1/x+1 = 1/20?

Answer 1

1 / x + - 1 / x + 1 = 1 / 20

1 / x - 1 / (x + 1) = 1 / 20

Multiply each side by x(x + 1)

x + 1 - x = x(x + 1) / 20

20 = x( x + 1)

x² + x - 20 = 0

x² + 5x - 4x - 20 = 0

x(x + 5) -4(x + 5) = 0

Take out common term x + 5

(x + 5)(x - 4) = 0

x - 4 = 0 or x + 5 = 0

x = 4 or -5.