Compound/complex fractional expressions. Algebra 1.

In summary: Thanks for the help!In summary, -xy is the unknown which needs to be solved for x^3y^2/y - x^2y^3/x is simplified to x^2y^2/x^2 - x^2y^2/y^2
  • #1
Hierophant
45
0

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
 
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  • #2
Hierophant said:

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).
Hierophant said:
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.
 
  • #3
Okay thanks for the corrections. I did mean x^2y^2.

I did end up solving it from that point.
 

1. What is a compound/complex fractional expression?

A compound/complex fractional expression is a mathematical expression that contains multiple fractions within it. These fractions may also have variables in the numerator and/or denominator, making the expression more complex.

2. How do I simplify a compound/complex fractional expression?

To simplify a compound/complex fractional expression, you should first find the common denominator for all of the fractions in the expression. Then, you can combine the fractions using the common denominator and perform any necessary operations, such as adding or subtracting the numerators. Finally, simplify the resulting expression as much as possible.

3. Can I cancel out common factors in a compound/complex fractional expression?

Yes, you can cancel out common factors in a compound/complex fractional expression. Just make sure that the factors you are canceling out are present in both the numerator and denominator of the fraction.

4. How do I solve equations with compound/complex fractional expressions?

To solve equations with compound/complex fractional expressions, you should first simplify the expression on both sides of the equation. Then, isolate the variable on one side of the equation using inverse operations. Finally, check your solution by plugging it back into the original equation.

5. What are some real-life applications of compound/complex fractional expressions?

Compound/complex fractional expressions can be used in many real-life scenarios, such as calculating the amount of medication needed for a patient based on their weight, determining the proportions of ingredients in a recipe, or calculating the cost of a discount or sale. They are also commonly used in engineering and science to represent complex mathematical models and equations.

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