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: