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### Rational Expressions and Functions: simplifying etc..

Posted: Fri Sep 20, 2013 1:36 am
I am taking an online math class and I have hit a huge bump on the road. I have two weeks left and I am freaking out! I can't seem to understand this at all. I took this class 10+ years ago and most of it comes back as soon as I see just a problem or two done step by step.

-7x^2/28x^5y is the first problem which for the life of me I can't do, I feel so dumb.

Does anyone konw how to do these?!

8x^2/x-9 times x^2+6x+9/16x^3

### Re: Rational Expressions and Functions: simplifying etc..

Posted: Fri Sep 20, 2013 4:01 am
I am taking an online math class and I have hit a huge bump on the road. I have two weeks left and I am freaking out! I can't seem to understand this at all. I took this class 10+ years ago and most of it comes back as soon as I see just a problem or two done step by step.

-7x^2/28x^5y is the first problem which for the life of me I can't do, I feel so dumb.

Does anyone konw how to do these?!

8x^2/x-9 times x^2+6x+9/16x^3
You give ambiguous expressions. You appear to be in need to remind yourself about rules of exponents and the meaning of 1 in rational form.

$\frac{-7x^2}{28x^5 \cdot y}\, =\, \frac{-1 \, \cdot \, 7\, \cdot \,x^2}{4\, \cdot \,7\, \cdot \,x^2\, \cdot \,x^3\, \cdot \,y}\, =\, \frac{-1 \, \cdot \, \cancel{7}\, \cdot \,\cancel{x^2}}{4\, \cdot \,\cancel{7}\, \cdot \,\cancel{x^2}\, \cdot \,x^3\, \cdot \,y}\,=\, \frac{-1}{4\, \cdot \,x^3\, \cdot \,y}\,=\, \frac{-1}{4x^3y}$

Posted: Fri Sep 20, 2013 10:56 am
Does anyone konw how to do these?!

8x^2/x-9 times x^2+6x+9/16x^3
Your formatting, lacking grouping symbols, is ambiguous. As posted, it means the following:

. . . . .$\left(\frac{8x^2}{x}\, -\, 9\right)\left(x^2\, +\, 6x\, +\, \frac{9}{16x^3}\right)$

However, I strongly suspect that you mean this:

. . . . .$\left(\frac{8x^2}{x\, -\, 9}\right)\left(\frac{x^2\, +\, 6x\, +\, 9}{16x^3}\right)$

As for how to simplify these fractions, one uses the usual method: factor, and cancel any common factors. The only real difference is that one is factoring quadratics and simplifying such as is shown in the previous reply, rather than working only with simple numerical values.