Compound/complex fractional expressions. Algebra 1.

[Hierophant]

Homework Statement

x/y - y/x
----------
1/x^2 - 1/y^2

Simplify the compound fractional exponent.

Homework Equations

The process that you are supposed to use are 1. finding the LCD and combining the expressions in the numerator and then the denominator, making it just a regular fractional expression.

So

2 - 1 1
--- = ----
2 - 1 1

Then you simplify from there, usually then multiplying the inverted divisor.

The second way is to find the LCD, then simply multiply the numerator and denominator.

So

x/y - y/x xy^2(apparent LCD)
---------- * -------
1/x^2 - 1/y^2 xy^2

Then you simplify from there.

The Attempt at a Solution

Here is my attempt:

x/y - y/x xy^2
---------- * -------
1/x^2 - 1/y^2 xy^2

Multiply the xy^2 into the four numerators.

left with

x^3y^2/y - x^2y^3/x
------------------------
x^2y^2/x^2 - x^2y^2/y^2

Which simplifies to:

X^3y -xy^3
--------------
y^2 - x^2

Factor out an (-xy)

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

Now the answer is -xy, so is it possible to have the rest of the equation to cancel out somehow?

I'm not sure where to go from here, but I am looking up other tutorials on how to solve this type of equation. It feels as though, I may be missing a detail or two, so if you could point this out to me, I'd definitely appreciate this.

If you need anymore information, I'd be glad to add some more.


Thanks

 

[Mark44]

Homework Statement

x/y - y/x
----------
1/x^2 - 1/y^2

Simplify the compound fractional exponent.

Homework Equations

The process that you are supposed to use are 1. finding the LCD and combining the expressions in the numerator and then the denominator, making it just a regular fractional expression.

So

2 - 1 1
--- = ----
2 - 1 1

Then you simplify from there, usually then multiplying the inverted divisor.

The second way is to find the LCD, then simply multiply the numerator and denominator.

So

x/y - y/x xy^2(apparent LCD)
---------- * -------
1/x^2 - 1/y^2 xy^2

Then you simplify from there.

The Attempt at a Solution

Here is my attempt:

x/y - y/x xy^2
---------- * -------
1/x^2 - 1/y^2 xy^2

Multiply the xy^2 into the four numerators.

left with

x^3y^2/y - x^2y^3/x
------------------------
x^2y^2/x^2 - x^2y^2/y^2

Which simplifies to:

X^3y -xy^3
--------------
y^2 - x^2

Factor out an (-xy)

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

Your mistake is above. The numerator should be (-xy)(-x² + y²).

Now the answer is -xy, so is it possible to have the rest of the equation to cancel out somehow?

I'm not sure where to go from here, but I am looking up other tutorials on how to solve this type of equation. It feels as though, I may be missing a detail or two, so if you could point this out to me, I'd definitely appreciate this.

If you need anymore information, I'd be glad to add some more.


Thanks

The LCD of all the denominators is x²y². Possibly that's what you meant when you wrote xy², but that just means x * y², not (xy)².

With regard to "is it possible to have the rest of the equation to cancel out somehow?" -- what you're working with is NOT an equation. You're simplifying an expression. An equation is two expressions connected with an = sign.

 

[Hierophant]

Okay thanks for the corrections. I did mean x^2y^2.

I did end up solving it from that point.