How do you solve (3x/y - x) divided by (y/x - y)?

Question

its 3x/y - x/1
not 3x / y-x

so.. to make it more obvious:
3x/y minus x

Answer 1

thanks for explaining that

((3x/y) - x)/((y/x) - y)
((3x - xy)/y)/((y - xy)/x)
(x(3x - xy))/(y(y - xy))
(x^2(3 - y))/(y^2(1 - x))

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but if you mean

((3x/y) - x)/(y/(x - y))

((3x - xy)/y)/(y/(x - y))
((3x - xy)/y)((x - y)/y)
(3x - xy)(x - y)
x(3 - y)(x - y)
x(3x - 3y - xy + y^2)
3x^2 - 3xy - x^2y + xy^2

Answer 2

Answer1:

3/(x-y) *(x-y)/y

=3/y
(This is the answer.) END.


Answer2:
multiply by xy
((3x/y - x) ) / ( (y/x - y))
=?

(3*x^2-x^2*y ) / (y^2-x*y^2)

=x^2*(3-y)/y^2*(1-x)

=(x/y)^2* ((3-y)/(1-x))

So, please use paranthesis whereever necessary.