fractions with unknowns

Question

In Algebra 1 I am given the following problem:

 

(2x - 1) / (x² - x - 6) - (x + 2) / (x - 3)

  
Please help me.

Answer 1

(2x - 1)/(x² - x - 6) - (x + 2)/(x - 3)

 

The first thing we need to do is factor out that quadratic, see what sort of things we need to multiply to get an equal denominator:

^{2x - 1}/_{(x - 3)(x + 2)} - ^{x + 2}/_{(x - 3)}

Since both sides already share a x-3, we need to multiply the latter ratio by x+2:

^{2x - 1}/_{(x - 3)(x + 2)} - ^{(x + 2)(x + 2)}/_{(x - 3)(x + 2)}

^{2x - 1}/_{(x - 3)(x + 2)} - (x² + 4x + 4)/_{(x - 3)(x + 2)}

Distribute that subtraction sign:

^{2x - 1}/_{(x - 3)(x + 2)} + (-x² - 4x - 4)/_{(x - 3)(x + 2)}

Now we can add/subtract:

(-x² - 2x - 5) / (x - 3)(x + 2)