## anonymous one year ago What is the solution to the rational equation x over x squared minus 9 plus 1 over x plus 3 equals 1 over 4x minus 12 ?

1. Nnesha

$\huge\rm \frac{ x }{ x^2-9}+\frac{ 1 }{ x+3}=\frac{ 1 }{ 4x-12 }$ like this ?

2. anonymous

yes

3. Nnesha

alright first solve left side apply difference of square method to factor x^2-9 $\rm a^2-b^2=(a+b)(a-b)$

4. Nnesha

take square of both terms write ur answer as (sqrt of 1st term + sqrt of 2nd term) (sqrt of 1st term - sqrt of 2nd term) here is an example $\rm x^2-16=(x+4)(x-4)$

5. anonymous

x = -9 over 7 x = 15 x = 15 over 7 x = 9

6. anonymous

these are the answers i have

7. Nnesha

ok. so what are the factors of x^2-9 ?

8. anonymous

(x-9)(x+9)

9. Nnesha

hmm not what is the square root of 9 ?

10. anonymous

3

11. Nnesha

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12. Nnesha

yes right so it should be (x-3)(x+3)

13. Nnesha

$\huge\rm \frac{ x }{ (x-3)(x+3)}+\frac{ 1 }{ x+3}=\frac{ 1 }{ 4x-12 }$ now find common denominator what is the common denominator at left side ?

14. anonymous

so 4(3)-12?

15. Nnesha

no.. common denominator$\huge\rm \frac{ x }{ \color{Red}{(x-3)(x+3)}}+\frac{ 1 }{\color{Red}{ x+3}}=\frac{ 1 }{ 4x-12 }$ just look at red part what is common ?

16. anonymous

3

17. Nnesha

its not just 3 (x-3) is one term so x+3 is common

18. Nnesha

.. $\huge\rm \frac{ x }{ \color{Red}{(x-3)(x+3)}}+\frac{ 1 }{\color{Red}{ x+3}}=\frac{ 1 }{ 4x-12 }$ $\huge\rm \frac{ x +1(x-3)}{ (x-3)(x+3) }$ when you find common denominator you should multiply numerator of 1st fraction by the denominator of 2nd fraction and multiply numerator of 2nd fraction by the denomiantor of 1st fraction

19. anonymous

$-\frac{ 9 }{ 7 }$

20. Nnesha

combine like terms .. $\huge\rm \frac{ x +1x-3}{ (x-3)(x+3) }$ x+1x-3= ??

21. anonymous

? is this right

22. Nnesha

what ??

23. Nnesha

no that's not right

24. Nnesha

what are like terms in this equation x+x-3 ?

25. anonymous

x

26. Nnesha

yes right so combine them x+x = ?

27. anonymous

x^2?

28. Nnesha

no when you multiply same bases then you should add their exponents no just add the coefficient 1x+1x=(1+1)x = ?

29. anonymous

im confused

30. Nnesha

okay so here we need to combine x+x which is same as 1x+1x one is invisible we here is an example 3y+5y = (3+5)y = 8y just add the coefficient $\rm x \times x=x^2$ when you multiply them then you should add their exponents

31. Nnesha

|dw:1440353412609:dw| leading coefficient a number front of the variable

32. Nnesha

1x+1x = ?

33. anonymous

1x

34. Nnesha

add their coefficient $1x+1x=(1+1)x= ??x$

35. anonymous

2x

36. Nnesha

yes right .. $\huge\rm \frac{ x }{ \color{Red}{(x-3)(x+3)}}+\frac{ 1 }{\color{Red}{ x+3}}=\frac{ 1 }{ 4x-12 }$ $\huge\rm \frac{ 2x-3}{ (x-3)(x+3) }=\frac{1}{4x-12}$ now foil this (x-3)(x+3) are you familiar with the foil method ?

37. anonymous

x = 9 is this right?

38. Nnesha

no... show ur work so i'll look ovr to find mistakes :=)

39. anonymous

idk i dont understand

40. Nnesha

so you don't know how to foil two parentheses ?

41. anonymous

ido x^2 +3x-3x-9?

42. Nnesha

yes right which is same as x^2-9 $\frac{ 2x-3 }{ x^2-9 }=\frac{ 1 }{ 4x+12 }$now cross multiply

43. Nnesha

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