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