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OpenStudy (anonymous):

2x^(2)-7x-4/x^(2) * 8x^(2)-28x+12/4x^(2)-1 Multiply

OpenStudy (anonymous):

@Hero

hero (hero):

Use the drawing pad please.

OpenStudy (anonymous):

ok

OpenStudy (anonymous):

\[\frac{ 2x^{2}-7x-4 }{ x ^{2} }\times \frac{ 8x ^{2}-28x+12 }{ 4x ^{2}-1 }\]

OpenStudy (anonymous):

@Mertsj

hero (hero):

Did you try factoring the numerators yet?

OpenStudy (anonymous):

let me do it reak quick n check

hero (hero):

Now cancel factors of one, then simplify

OpenStudy (anonymous):

all my sign were opposite than yours

OpenStudy (anonymous):

how do i simplify

hero (hero):

To simplify: 1. Cancel all factors of 1 2. Combine the product of both fractions into one fraction

OpenStudy (anonymous):

\[\frac{ x+4 }{ x ^{2} } \times \frac{ 4(x-3) }{ 2x+1 }\] this?

hero (hero):

You can only eliminate one set of factors of one at a time

hero (hero):

You can't eliminate every (2x - 1) you see. That's not how it works.

hero (hero):

Also, you need to combine everything into just one fraction. For example, if you have \[\frac{a}{b}×\frac{c}{d}\] When you combine that into one fraction, you'll have \[\frac{ac}{bd}\]

hero (hero):

When you simplify the product of two fractions, you want to express your answer in the form of one fraction with no common factors. A factor of one is a fraction such that you have the same number in the numerator and denominator: \[\frac{a}{a}\] You can only eliminate one common factor at a time. If you have \[\frac{aa}{a}\] Then you simplify as follows: \[\frac{aa}{a} = \frac{a\cancel{a}}{\cancel{a}} = a\]

hero (hero):

Notice that you don't cancel all the a's. Only the factors of one

hero (hero):

Also \[\frac{aa}{a} = a \times \frac{a}{a} = a \times 1 = a\]

OpenStudy (anonymous):

so whats the answer

OpenStudy (anonymous):

@Hero

OpenStudy (anonymous):

...

hero (hero):

Tell me what you think the answer is first.

OpenStudy (anonymous):

\[\frac{4(x-4) }{x+3 }\]

OpenStudy (anonymous):

@Hero

hero (hero):

Okay, I made a sign error earlier. I apologize.

hero (hero):

After factoring you should get: \[\frac{(2x+1)(x-4)}{x^2} \dot\ \frac{4(2x-1)(x-3)}{(2x+1)(2x-1)}\]

OpenStudy (anonymous):

so my answer wasnt right

hero (hero):

Next rewrite in a way so that the factors of one are lined up one on top of the other: \[\frac{(2x+1)(2x-1)}{(2x+1)(2x-1)} \dot\ \frac{4(x-4)(x-3)}{ x^2}\] Then cancel factors of 1: \[\frac{\cancel{(2x+1)(2x-1)}}{\cancel{(2x+1)(2x-1)}} \dot\ \frac{4(x-4)(x-3)}{ x^2}\] Now you're left with the correct result: \[\frac{4(x-4)(x-3)}{ x^2}\]

OpenStudy (anonymous):

that it?

hero (hero):

Yes, that should be it. But sometimes, they want the expanded form.

hero (hero):

You'll have to multiply the numerator in order to get that.

OpenStudy (anonymous):

thats not an option on a b c or d

hero (hero):

I just explained to you that you might have to multiply the numerator in order to get the expanded form.

hero (hero):

Try it and see

OpenStudy (anonymous):

idk how

OpenStudy (anonymous):

A) \[\frac{ x-16 }{ x+3 }\] B)\[\frac{ x-4 }{ x+3 }\] c)\[\frac{ 4(x-4) }{ x+3 }\] D)\[\frac{ 4x-4 }{ x+3 }\]

hero (hero):

You must have posted the original problem incorrectly. There's no way you get x + 3 in the denominator.

hero (hero):

Double check that that original question and the answer choices are for the same problem.

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