Question

what is the sum of the rational expressions below? 2x-1/7x + x/x-2
a. 9x^2-5x+2/7x^2-2
b. 9x^2-5x+2/7x^2-14x
c. 3x-1/8x-2
d. 2x^2-5x+2/7x^2-14x

Answer 1

x-4/2x=3x/2x-1 (invert the bottom and then multiply) 
x-4 (2x+3x/2x-1) ( the 2x's cancel) 
x-4 (3x/-1) 
x-4 (-3x) (expand) 
-3x^2 + 12x=0 
-3x^2= -12x (bring 12x to other side making it negative) 
-3x^2/3x= -12x/-3x (divide both sides by -3x) 
x=4 
Hope that helps

Answer 2

$\frac{2x-1}{x} + \frac{x}{x -2} = \frac{(2x-1)(x-2) +(x)(7x)}{(7x)(x-2)}$

You know the first term of the numerator wil be 2x^2 +7x^2 = 9x^2, and the last term of the denominator will be 7x(-2) = -14x.

This is sufficient work to identify selection B as the correct choice.