Can someone help me with this:
(x^2y^(-2)-y^2x^(-2))/(xy^(-1)-yx^(-1))
Please and thank you
if this is still confusing tell me I'll try to clear it up more if I can
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)
is this right so far?
Next Step:
[2(x^3)(y)-2(y^3)(x)]/[(x^2)(y)-(x)(y^2)]
please comfirm this
(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)
how did you get this: [ (x^4 - y^4)/(x^2 y^2) ]
ok I know how you got (x^2 y^2) but, how did you get (x^4 - y^4)???
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.
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.
thank you for your help I really appreciate it
Certainly! Let's simplify the expression step by step.
First, let's simplify the numerator:
(x^2y^(-2) - y^2x^(-2))
To simplify this expression, we can factor out a common factor of "x^(-2)":
x^(-2)(xy^(-2) - y^2)
Next, let's simplify the denominator:
(xy^(-1) - yx^(-1))
Similarly, we can factor out a common factor of "xy^(-1)":
xy^(-1)(1 - yx^(-2))
Now, let's rewrite our expression using the simplified numerator and denominator:
[x^(-2)(xy^(-2) - y^2)] / [xy^(-1)(1 - yx^(-2))]
Next, let's simplify further by canceling out common factors between the numerator and denominator. We can see that "xy^(-2)" and "xy^(-1)" can be canceled out:
Canceling out common factors: (y^(-2) - y^2) / (1 - yx^(-2))
Now, let's simplify each of the terms separately.
Starting with the numerator, let's factor out a common factor of "y^(-2)":
y^(-2)(1 - y^4)
Now, let's simplify the denominator by distributing the negative sign:
1 - yx^(-2)
Finally, our simplified expression becomes:
(y^(-2)(1 - y^4)) / (1 - yx^(-2))
And that's the simplified expression!