What am I doing wrong? (Simplifying Rational Expressions)

In summary: Multiply the First terms: . (-5xy)(2xy) \:=\: -10x^2y^2 Multiply the Inner terms: . (-5xy)(y^2) \:=\: -5xy^3 Multiply the Outer terms: . (4y^2)(2xy) \:=\: 8xy^3 Multiply the Last terms: . (4y^2)(y^2) \:=\: 4y^4 Combine the results: . (-10x^2y^2 - 5xy^3 + 8xy^3 + 4y^4) Then you said: .-3xy^3+28y^4
  • #1
eleventhxhour
74
0
7a) Simplify and state any restrictions on the variables:

\(\displaystyle \frac{x^2-5xy+4y^2}{x^2+3xy-28y^2} ⋅ \frac{x^2+2xy+y^2}{x^2-y^2} \)

I'm not really sure what a good process would be to simplify this. This is what I tried to do, (below) which is wrong. Could anyone point out what I did wrong and what a better process to simplify it would be? Thanks!

My answer:

\(\displaystyle \frac{-5xy+4y^2}{3xy-28y^2} ⋅ \frac{2xy + y^2}{-y^2}\)

\(\displaystyle \frac{-10x^2y^2 + 4y^4}{-3xy^3+28y^4}\)

\(\displaystyle \frac{2y^2(-5x^2+2y^2}{y^3(-3x+28y)}\)

And then I'm not sure what to do.
 
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  • #2
I would suggest factoring first, and then from this you can see the restrictions and then simplify:

\(\displaystyle \frac{(x-y)(x-4y)}{(x+7y)(x-4y)}\cdot\frac{(x+y)^2}{(x+y)(x-y)}\)
 
  • #3
Hello, eleventhxhour!

What are you doing wrong? . . . Everything!


Simplify: .\(\displaystyle \frac{x^2-5xy+4y^2}{x^2+3xy-28y^2} ⋅ \frac{x^2+2xy+y^2}{x^2-y^2} \)
You have: .\(\displaystyle \frac{x^2-5xy+4y^2}{x^2+3xy-28y^2} ⋅ \frac{x^2+2xy+y^2}{x^2-y^2} \)

Then you canceled illegally:

. . \(\displaystyle \frac{{\color{red}\rlap{//}}x^2-5xy+4y^2}{{\color{red}\rlap{//}}x^2+3xy-28y^2} ⋅ \frac{{\color{red}\rlap{//}}x^2+2xy+y^2}{{\color{red}\rlap{//}}x^2-y^2} \)

And got: .\(\displaystyle \frac{-5xy+4y^2}{+3xy-28y^2} ⋅ \frac{+2xy+y^2}{-y^2} \)Then you multiplied incorrectly.

You said: .\(\displaystyle (-5xy + 4y^2)(2xy + y^2) \:=\:-10x^2y + 4y^4\)

. . as if you never heard of "FOIL".
 

Related to What am I doing wrong? (Simplifying Rational Expressions)

1. What does it mean to simplify rational expressions?

Simplifying rational expressions means to rewrite them in their simplest form by canceling out common factors in both the numerator and denominator.

2. How do I know if I have simplified a rational expression correctly?

You can check if you have simplified a rational expression correctly by plugging in values for the variables and simplifying the expression further. If the result is the same, then you have simplified it correctly.

3. Can I simplify a rational expression with variables in the denominator?

Yes, you can simplify a rational expression with variables in the denominator by factoring out the common factors and canceling them out, just like you would with variables in the numerator.

4. Why is it important to simplify rational expressions?

It is important to simplify rational expressions because it makes them easier to work with and understand. Simplified expressions also have the lowest possible degree, which makes them more useful for solving equations and graphing.

5. What are some common mistakes when simplifying rational expressions?

Some common mistakes when simplifying rational expressions include not factoring completely, forgetting to simplify negative signs, and canceling out terms that are not common factors.

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