Simplify the equation

Question

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

Answer 1

Zach, we have to first find a common denominator.

 

If we factor x² - 3x + 2, we get (x - 1)(x - 2). This will be our common deniminator.

 

In order for the first term to have this denominator, we have to multiply the numerator and denominator by (x - 2).

 

x(x -2)/(x - 1)(x - 2) = x² - 2x/(x - 1)(x - 2)

 

Now we add, combining our numerators over one denominator...

 

x² - 2x + 2x - 1/(x - 1)(x - 2) = x² - 1/(x - 1)(x - 2) = (x - 1)(x + 1)/(x - 1)(x - 2) = x + 1/x - 2

 

Hope this helps!