## anonymous one year ago Classify the solutions of 3 over x plus 5, plus one fifth, equals 2 over x plus 5 as extraneous or non-extraneous.

1. anonymous

@Algorithmic @ganeshie8 @CaptainLlama49

2. anonymous

3. Mertsj

I have typed this twice and lost it both times. I will try one more time.

4. anonymous

ok:)

5. Mertsj

$\frac{3}{x+5}+\frac{1}{5}=\frac{2}{x+5}$

6. Mertsj

Common denominator is 5(x+5). Multiply each term by that.

7. anonymous

so you get 15/5(x+5)+x+5/5(x+5)=10/5(x+5)

8. Mertsj

$5(x+5)(\frac{3}{x+5})+5(x+5)(\frac{1}{5})=5(x+5)(\frac{3}{x+5})$

9. Mertsj

Cancel all the denominators.

10. Mertsj

$15 +x+5=10$

11. anonymous

yup! :)

12. Mertsj

The 3 on the right side is supposed to be a 2

13. Mertsj

$x=-10$

14. Mertsj

Now. Is that extraneous or not? Does it cause any denominator to be 0? Does it make the original equation true?

15. anonymous

extraneous?

16. Mertsj

Why is it extraneous?

17. anonymous

3/ -5 +1/5 = 2/-5

18. anonymous

I don't know. When i plugged it in, that's the equation I got above,

19. Mertsj

$-\frac{3}{5}+\frac{1}{5}=-\frac{2}{5}$

20. Mertsj

Is that true or not?

21. Mertsj

Is any denominator equal to 0 ?

22. anonymous

no

23. Mertsj

Then it is a perfectly fine solution and is not extraneous.

24. anonymous

Oh!

25. anonymous

Thank you:)

26. anonymous

27. Mertsj

An extraneous solution is a number that appears to be a solution but doesn't hold up to scrutiny because it either doesn't check or causes a denominator to be 0.

28. Mertsj

Yes

29. anonymous

Solve for x: 2 over 5 plus 3 over 5 x equals quantity x plus 5 over 10.

30. anonymous

Okay! I understand now:)

31. anonymous

For this one, I got x=-3,2

32. Mertsj

$\frac{2}{5}+\frac{3}{5x}=\frac{x+5}{10}$

33. Mertsj

Is that it?

34. anonymous

yeah:)

35. Mertsj

$10x(\frac{2}{5})+10x(\frac{3}{5x})=10x(\frac{x+5}{10})$

36. Mertsj

$4x+6=x^2+5x$

37. anonymous

-1x^2+5x+36

38. Mertsj

$x^2+x-6=0$

39. Mertsj

$(x+3)(x-2)=0$

40. anonymous

So, -3 and 2 ?

41. Mertsj

$x=-3,2$

42. anonymous

Last one:)?

43. Mertsj

$\frac{2}{5}+\frac{3}{5(-3)}=\frac{-3+5}{10}$

44. Mertsj

$\frac{2}{5}-\frac{3}{15}=\frac{2}{10}$

45. Mertsj

$\frac{2}{5}-\frac{1}{5}=\frac{1}{5}$

46. Mertsj

That seems to check. Try 2. See if it checks.

47. anonymous

Okay, that makes sense!! :D

48. anonymous

Classify the solutions of 1 over x plus 4, plus one half, equals 1 over x plus 4 as extraneous or non-extraneous.

49. anonymous

So, I got -4

50. Mertsj

$\frac{1}{x+4}+\frac{1}{2}=\frac{1}{x+4}$

51. Mertsj

And -4 causes the denominator to be 0 so it is extraneous.

52. anonymous

yes, I agree

53. Mertsj

Good job!!

54. anonymous

Solve for x: 1 over 2 plus 4 over 2 x equals quantity x plus 4 over 10.

55. Mertsj

Me too. Did you check them?

56. Mertsj

They both check.