How do you simplify \frac { x + 5y } { x + 3y } - \frac { 2x + y } { 3y + x } + \frac { 4x + 5y } { x + 3y }?

1 Answer
Sep 19, 2017

3

Explanation:

Since all the denominators are equal, we can just combine the numerators together from
(x+5y)/(x+3y)-(2x+y)/(3y+x)+(4x+5y)/(x+3y) to

(x+5y-(2x+y)+4x+5y)/(x+3y).

Let's work on the numerator first. First, we remove the brackets

x+5y -2x-y +4x+5y

Then group like terms.

x-2x+4x+5y -y +5y

x+4x-2x =3x" " and " "5y-y+5y=9y

The expression will now be 3x+9y.

Put them all together as a fraction and you get (3x+9y)/(x+3y).

Next, we will factor out the common term, which is 3, to get

(3(x+3y))/(x+3y).

We will cancel out x+3y.

(3(cancel(x+3y)))/(cancel(x+3y))=3.

The answer is 3.