Question

Solve for x. 3/x-1 - 1/x^-1=5/x-1

Please show all work

Answer 1

x = -3/2

Explanation:

`(3(x+1))/((x-1)(x+1)) - (1)/((x-1)(x+1)) = (5(x+1))/((x-1)(x+1)) \\` Find the common denominator

3(x+1) - 1 = 5(x+1) Distribute

3x + 3 -1 = 5x +5 Combine Like terms

3x + 2 = 5x + 5 Solve for x

2 = 2x +5

-3 = 2x

x = -3/2

Answer 2

3/(x-1) - 1/(x^2-1) = 5/(x-1)

Subtract 3/(x-1) from both sides

-1/(x^2-1) = 2/(x-1)

Factor x^2 - 1

-1/[(x-1)(x+1] = 2/(x-1)

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

-1 = 2 (x+1)

-1 = 2x + 2

Subtract 2 from both sides

-3 = 2x

Divide by 2 on both sides

-3/2 = x