# How do you combine #[(2x + y)/(x - y)] - [(3x - y)/(x + y)] - [(5x + 2y)/(y^2 - x^2)]#?

##### 2 Answers

Given:

**Step 1**: determine an appropriate common denominator

Since

**Step 2**: Evaluate the numerators by multiplying each by the factor needed to obtain the common denominator

It is probably easiest to evaluate each numerator term separately then recombine

Giving a numerator sum of

**Step 3**: Recombine as a final solution

We can find the lowest common denominator for your fractions. In order to do that, we'd better factor the third fraction's denominator, as it's a squared product and the others have degree one (

By factoring laws, we know that if

We can see that this fits as l.c.d for the second fraction's denominator (due to the term

So, our l.c.d. will be

Now, rewriting the third fraction and then proceeding to the calculation:

Aggregating and simplifying signals and factors: