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## anonymous one year ago Find the difference and simplify: 2/(x^2+3x) - 3/(x^2-9)

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1. Nnesha

$\huge\rm \frac{ 2 }{ x^2+3x }-\frac{ 3 }{ x^2-9 }$ factor the denominator

2. anonymous

X(x+3)(x-3) ??

3. Nnesha

for x^2-9 apply the difference of squares $\huge\rm a^2-b^2=(a+b)(a-b)$ do you mean x(x+3)(x-3) is a common denominator ?

4. anonymous

Yes

5. Luigi0210

I think he went straight to the common denominator (:

6. Nnesha

true >.<

7. anonymous

Would the answer be -1/ x(x+3)(x-3) ??

8. Nnesha

alright then when we find common denominator we should multiply the numerator of 1st fraction with the denominator of the 2nd fraction and multiply the numerator of 2nd fraction with the denominator of first fraction (just like cross multiplication ) here is an example |dw:1442889917081:dw|

9. Nnesha

hmm no how did you get that ?

10. Nnesha

show ur work plz so i can find ot the mistakes :=)

11. anonymous

I just subtracted 2-3 and got -1 and used the common denominator. I actually dont know what im doing but im trying

12. Mertsj

$\frac{2}{x(x+3)}\times\frac{x-3}{x-3}-\frac{3}{(x-3)(x+3)}\times\frac{x}{x}$

13. Nnesha

hm no you can't do that

14. anonymous

Explain please?

15. Nnesha

just like i said multiply the numerator of first fraction with the denominator  of 2nd fraction so $\huge\rm \frac{ 2 }{ x(x+3) } -\frac{ 3 }{ (x+3)(x-3) }$ x(x+3)(x-3) is a common denominator so multiply first fraction with x-3 and 2nd fraction with x

16. anonymous

Would the numerator be x+6??

17. Nnesha

$\huge\rm \frac{ 2(x-3)-3(x) }{ x (x+3)(x-3)}$ distribute the parentheses by 2 and then combine like terms

18. Nnesha

2(x-3) = ?

19. anonymous

2x-6

20. Nnesha

yes right so $\huge\rm \frac{\color{Red}{ 2x-6-3x} }{ x (x+3)(x-3)}$ now combine like terms

21. anonymous

Would it he -x-6 / x(x+3)(x-3) ?!?!

22. Nnesha

yes right "=)

23. anonymous

Omg thank you so much!

24. Nnesha

np :=)

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