How do you simplify \frac{x-5y}{x+y}+\frac{x+7y}{x+y}x5yx+y+x+7yx+y?

1 Answer

(x - 5y)/(x + y) + (x + 7y)/(x + y) = 2x5yx+y+x+7yx+y=2

Explanation:

Because the denominators are the same, one can just add the numerators over the common denominator:

(x - 5y + x + 7y)/(x + y) = (2x + 2y)/(x + y)x5y+x+7yx+y=2x+2yx+y

Factor out (x + y)(x+y) from the numerator:

(2(x + y))/((x + y)) = 22(x+y)(x+y)=2

The simplest form is:

(x - 5y)/(x + y) + (x + 7y)/(x + y) = 2x5yx+y+x+7yx+y=2