## anonymous one year ago Simplify and select the answer with the appropriate restrictions for the variables

1. anonymous

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2. mathstudent55

Factor the numerator and denominator.

3. anonymous

@Michele_Laino

4. anonymous

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5. anonymous

@Michele_Laino

6. anonymous

what do you think? @Michele_Laino

7. Michele_Laino

please, solve the subsequent quadratic equation, first: ${x^2} - 2x - 8 = 0$

8. anonymous

how do you do that? @Michele_Laino

9. welshfella

this will factor to the form (x + a)(x + b) where ab = -8 and a + b = -2 can you find what a and b will be?

10. anonymous

8 and 2? since, (8+-8)(2+-2)=0

11. Michele_Laino

alternatively, you can apply the standard formula, so you have to compute this: $x = \frac{{2 \pm \sqrt {{2^2} - 4 \times 1 \times \left( { - 8} \right)} }}{2}$

12. welshfella

no that won't fit factoring -8 will help:- -8 = -4 * 2 or -8 = 4 * -2 which ons will give you -2 when added?

13. anonymous

-2 and 1?

14. anonymous

@Michele_Laino

15. Michele_Laino

I got: 4, and -2

16. anonymous

oh ok

17. Michele_Laino

so we can write this factorization: ${x^2} - 2x - 8 = \left( {x - 4} \right)\left( {x + 2} \right)$

18. anonymous

i got d?

19. Michele_Laino

substituting into your expression, we get: $\frac{{3{x^2} + 6x}}{{{x^2} - 2x - 8}} = \frac{{3x\left( {x + 2} \right)}}{{\left( {x - 4} \right)\left( {x + 2} \right)}}$

20. anonymous

nvm bc it has to match up to -4 and 2

21. Michele_Laino

that's right, it is option D

22. anonymous

wait so is it -4 and 2 or 4 and -2

23. welshfella

-4 and 2 - in order to get the -2x

24. anonymous

i will tag you in my next question!!:D

25. mathstudent55

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