Match the rational expressions with their rewritten form x2+4x-7/x-1, 2x2-3x+7/x-1, 2x2-x-7/x-1, x2-2x+7/x-1?

A (x+5) + - 2/x-1

B (x-1) + 6/x-1

C (2x+1) + - 6/x-1

D (2x-1) + 6/x-1

The easy way to do this problem is to start with the choices. What we will do is to expand the choices back to their original form.

A. (x+5) + - 2/x-1 = 0

Multiplying both sides by x - 1

(x-1) (x+5) - 2 = 0

x^2 + 5x - x - 5 - 2 = 0

x^2 + 4x - 7 = 0

Multiplying both sides by (1/x-1)

x^2 + 4x - 7 / x-1

B. (x-1) + 6/x-1 = 0

Multiplying both sides by x - 1

(x-1) (x-1) + 6 = 0

x^2 - x - x + 1 + 6 = 0

x^2 - 2x + 7 = 0

Multiplying both sides by (1/x-1)

x^2 - 2x + 7 / x-1

C. (2x+1) + - 6/x-1 = 0

Multiplying both sides by x - 1

(x-1) (2x+1) - 6 = 0

2x^2 + x - 2x - 1 - 6 = 0

2x^2 - x - 7 = 0

Multiplying both sides by (1/x-1)

2x^2 - x - 7 / x-1

D. (2x-1) + 6/x-1

Multiplying both sides by x - 1

(x-1) (2x-1) + 6 = 0

2x^2 - x - 2x + 1 + 6 = 0

2x^2 - 3x + 7 = 0

Multiplying both sides by (1/x-1)

2x^2 - 3x + 7 / x-1