How do you solve 1 + (2+x-y)/(x+y) = 2/y?

1 Answer
Mar 10, 2017

x=0 or y=1

Explanation:

First rearrange the equation to put the fractions together:

1=2/y-(2+x-y)/(x+y)

Multiply out the denominators. This can be done in one step, but I've done it in two to show exactly what's happening:

Multiply out x+y:

1(x+y)=(2(x+y))/y-(2+x-y)

Multiply out the y:

1(x+y)y=2(x+y)-y(2+x-y)

Simplify:

xy+y^2=2x+2y-2y-xy+y^2

xy+xy+cancel(y^2)=2x+cancel(2y)-cancel(2y)+cancel(y^2)

2xy=2x

2xy-2x=0

2x(y-1)=0

and dividing by 2 we get x(y-1)=0

as product of x and (y-1) is 0. we have

x=0 or y=1