## Tati_Lee 3 years ago Simplify completely

1. Tati_Lee

$\frac{ 5x ^{2}+9x-2 }{ x ^{2}+12x+20 } * \frac{ x ^{2}+17x+70 }{ 15x-3 }$

2. ghass1978

can you factorize the respective numerators and denominators?

3. Tati_Lee

no, thats all i need help with & i can do the rest

4. ghass1978

look for example at 5x^2+9x-2 look for 2 numbers whose product is -2*5=-10 and whose sum is 9

5. AidanNims

((x+2)(5x-1))/(x+10)(x+2)* ((x+7)(x+10)/3(5x-1) the way u apporach them is what numbers multiply to give lets say 70... well 7 and 10 . do they add to form the 17x yes cause 10 +7+17.

6. Compassionate

$\frac{ (x+2)(5x+1) }{ (x+10)(x+2)} * \frac{ (x+10)(x+7) }{ 3(5x+1) }$ (5x+1) cancels (x + 10) cancels $\frac{ x+2 }{ x+2 } * \frac{ x+7 }{ 3} = 1 * \frac{ x + 7 }{ 3 } = \frac{ x+7 }{ 3 }$ This, I cannot factor anymore.

7. Tati_Lee

thank you @AidanNims & @Compassionate

8. Tati_Lee

can you help me with one more @Compassionate ?

9. Compassionate

Yea.

10. Tati_Lee

great! .. hold on let me write it out

11. Tati_Lee

$\frac{ x ^{2}+x-12 }{ x ^{2}-x-20 }\div \frac{ 3x ^{2}-24x+45 }{ 12x ^{2}-48x-60}$

12. Compassionate

One sec, putting on music then I'll solve it. c:

13. Tati_Lee

okie dokie

14. Compassionate

Do you want me too factor it, or just give you the answer?

15. Tati_Lee

you can just give me the answer lol

16. Compassionate

Damn, this expression is walking all over me.

17. Compassionate

$\frac{ (x+4)(x-3) }{ (x+4)(x-5) } - \frac{ 3(x-3)(x-5) }{ 4(3x^2-x-5) }$

18. Compassionate

After this part I know what too do, I just can't figure out of to construct a common denominator.

19. Tati_Lee

okay thank you so much!