Question

Why does

X(x+y) - y(x+y)/ x-y

factor to (x+y)(x-y)/x-y

Answer 1

\[X(x+y) - y(x+y)/x-y = (x+y)(x-y)/x-y\]

Answer 2

where does the x and -y go?

Answer 3

Is X different from x?

Answer 4

no

Answer 5

factoring out (x+y) in the numerator we get\[\frac{x(x+y)-y(x+y)}{x-y}=\frac{(x+y)(x-y)}{x-y}=x+y\]

Answer 6

but factoring out the x+y 's give you 1

Answer 7

try distributing (x+y) as a whole into
(x+y)(x-y)so it works in reverse as well