Question

Can someone help me with this:

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

Please and thank you

Answer 1

if this is still confusing tell me I'll try to clear it up more if I can

Answer 2

would this be the next step?

[(x^2)(2/y)-(y^2)(2/x)]/[(x)(1/y)-(y)(1/x)]
multiply the top and bottom by (xy)

Answer 3

is this right so far?

Next Step:
[2(x^3)(y)-2(y^3)(x)]/[(x^2)(y)-(x)(y^2)]

please comfirm this

Answer 4

(x^2y^(-2)-y^2x^(-2))/(xy^(-1)-yx^(-1))
= [ (x^4 - y^4)/(x^2 y^2) ] / [(x^2 - y^2)/(xy) ]
= (x^4 - y^4)/(x^2 y^2) *(xy)/(x^2 - y^2)
= (x^2 + y^2)(x^2 - y^2)/(x^2 y^2) * (xy)/(x^2 - y^2)
= (x^2 + y^2)/(xy)

Answer 5

how did you get this: [ (x^4 - y^4)/(x^2 y^2) ]

Answer 6

ok I know how you got (x^2 y^2) but, how did you get (x^4 - y^4)???

Answer 7

Now the more I think about it I'm a little confuse here: [ (x^4 - y^4)/(x^2 y^2) ] / [(x^2 - y^2)/(xy) ]
I just don't know how you did the first step but the rest I understand.

Answer 8

look at x^2/y^2 - y^2/x^2
we need a common denominator of x^2y^2

so the above is
(x^4 - y^4)/(x^2y^2)

same thing for the bottom of the original
I then factored the top as a difference of squares

x^4 - y^4 = (x^2 + y^2)(x^2 - y^2)

a lot of the stuff then canceled.

Answer 9

thank you for your help I really appreciate it