## anonymous one year ago What is the simplified form of x plus 2 over x squared minus 3x minus 10 • x minus 3 over x squared plus x minus 12 ? 1 over the quantity x minus 3 times the quantity x plus 4 1 over the quantity x minus 3 times the quantity x plus 2 1 over the quantity x plus 4 times the quantity x minus 5 1 over the quantity x plus 2 times the quantity x minus 5

1. anonymous

$\frac{ x + 2 }{ x^2 - 3x - 10 } \times \frac{ x - 3 }{ x^2 + x -12 }$

2. anonymous

@iGreen do i flip the 2nd fraction then horizontally multiply ?

3. iGreen

No, that was for division..you can horizontally multiply now.

4. anonymous

oh okay

5. anonymous

quick question when we horizontally multipl would the numerator be x^2 + 2 -3 or x+ 2 x- 3?

6. iGreen

None.. $$\sf (x+2)(x-3)$$ x * x = ? x * -3 = ? 2 * x = ? 2 * -3 = ?

7. anonymous

x^2 -3x 2 -6

8. iGreen

Actually, first we cancel the common factors.

9. anonymous

for the denominator ?

10. iGreen

For the 2nd fraction

11. iGreen

1st*

12. iGreen

Factor $$\sf x^2 - 3x - 10$$ from the numerator..tell me what you get.

13. iGreen

Can you do that?

14. anonymous

is it x/ x^2 - 3x -5

15. iGreen

No..

16. iGreen

Can you factor $$\sf x^2 - 3x - 10$$?

17. anonymous

oh yeah give me sec

18. iGreen

Okay

19. anonymous

(x + 2) (x - 5)

20. iGreen

Yes, so we have: $$\sf \dfrac{x+2}{(x-5)(x+2)} \times \dfrac{x-3}{x^2+x-12}$$ The x + 2's cancel out, giving us: $$\sf \dfrac{\cancel{x+2}}{(x-5)(\cancel{x+2})} \times \dfrac{x-3}{x^2+x-12}$$ $$\sf \dfrac{1}{(x-5)} \times \dfrac{x-3}{x^2+x-12}$$

21. iGreen

Now we multiply horizontally..but first factor $$\sf x^2 + x - 12$$.

22. anonymous

(x - 3) (x + 4)

23. anonymous

but it would be $\frac{ 1 }{ (x - 5) } \times \frac{ 1 } { ( x + 4)}$

24. iGreen

Yes..which gives us: $$\sf \dfrac{1}{(x-5)(x+4)}$$

25. iGreen