How do you solve #1 + (2+x-y)/(x+y) = 2/y#?
1 Answer
Mar 10, 2017
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
#1(x+y)=(2(x+y))/y-(2+x-y)#
Multiply out the
#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
as product of