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andriod09 3 years ago I need help on a Factoring problem. Its factoring a fraction, on top of another factoring fraction. Its in the comments

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1. andriod09

$\huge\frac{\frac{30x^2+27x+6}{9x^2-49}}{\frac{30x+15}{30x-70}}$

2. SmoothMath

The size of those fraction bars is important. The top two appear to be the same length, and the third is smaller. Correct?

3. strawberry17

To factor the numerator of the top fraction, you would divide each number by 3 and get: 3(10x^2 + 9x +2)

4. andriod09

no, the fracton bar on the top is supposed to be in the middle, i.e. it should be the top fraction normal bar, then solid black bar, then bottom fraction normal. @strawberry17 how would i do that?

5. SmoothMath

$$\Huge \frac{30x^2+27x+6}{9x^2-49} \div\frac{30x+15}{30x-70}$$ $$\Huge =\frac{30x^2+27x+6}{9x^2-49} *\frac{30x-70}{30x+15}$$

6. andriod09

its supposed to be: $\frac{30x^2+27x+6}{9x^2−49}$ over with the solid black line, $\frac{30x+15}{30x−70}$

7. SmoothMath

Like I put, Andriod?

8. andriod09

i don't understand what you did.

9. SmoothMath

One fraction divided by another fraction.

10. andriod09

i don't know. i tried to put it like it is in the book. thats what it says,

11. andriod09

yes, but i get very confused with fraction.

12. SmoothMath

Okay, Andriod, when we divide by a fraction, it's the same as multiplying by the reciprocal. That is, $$\div 2$$ is the same as $$\large *\frac{1}{2}$$ $$\large \div\frac{2}{3}$$ is the same as $$\large *\frac{3}{2}$$

13. SmoothMath

etc. So when we see $$\huge\div \frac{30x+15}{30x-70}$$ it's easier for us if we rewrite it as $$\huge *\frac{30x-70}{30x+15}$$

14. andriod09

ik that much, but i don't know what to do wit hthe FRACTIONS, i.e. i know the KFC method, but what/how do i factor the fraction?

15. strawberry17

@andriod09 do you understand how I factored out 3 from the numerator of the top fraction?

16. SmoothMath

What does KFC stand for?

17. andriod09

K=keep F=flip C=change @strawberry17 i have not a clue.

18. SmoothMath

Andriod, look for a common factor. With $$30x^2 + 27x + 6$$ you can notice that 30=3*10 27= 3*9 6= 3*2 so they have a common factor of 3.

19. SmoothMath

I agree, Strawberry. Rewriting it is good, but it's good to keep it factored as it is.

20. andriod09

i don't understand. $:($$:L$$:/$

21. andriod09

yes. i undertand what factoring is. I don't konw how to factor a fraction. hence, why this post is here.

22. andriod09

FACTORING A FRACTION IS ALL I DO NOT KNOW. I KNOW HOW TO FACTOR SOMETHING LIKE THIS: $x^2+3-27$

23. SmoothMath

Factoring a fraction is not different from factoring normally. Just look at the top and factor it normally. Then look at the bottom and factor it normally.

24. andriod09

I DON'T KNOW HOW. :/

25. andriod09

I DON'T KNOW HOW TO FACTOR A FRACTION.

26. andriod09

just tell me how to do this problem please, i am getting really annoyed.

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