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Question 266289: Good morning guys
This is my equation (under the rational expression section in my textbook)
Simplify (2x^3-2x^2-12x)(x^4-2x^3-8x^2)^-1 (That is a negative one)
What I've done so far
Factored both polynomials
(2x^2-2x)(x+6)
_____________
(x^2+2x)(x^2+4x^2)
Since it is a -1 I followed the text book instructions and put
(2x^2-2x)(-1)(6+x)
_______________
(x^2+2x)(x^2+4x^2)
That's where I lose track.
Any help is welcome. Thank you very much!
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website!
When you have something like:
a^(-2)
To make it a positive exponent you can move it to the denominator:
1/a^2
.
Similarly:
1/a^(-2)
To make it a positive exponent, move it the numerator:
a^2
.
Your problem then:
(2x^3-2x^2-12x)(x^4-2x^3-8x^2)^-1
can be written as a fraction:
(2x^3-2x^2-12x)
-----------------
(x^4-2x^3-8x^2)
.
Now, factoring out what's common:
2x(x^2-x-6)
-----------------
x^2(x^2-2x-8)
.
2x(x-3)(x+2)
-----------------
x^2(x-4)(x+2)
.
Canceling like-terms, we get:
2(x-3)
--------
x(x-4)
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