## anonymous 3 years ago can someone show me the steps to solve x/6=x/7+5

1. anonymous

multiply with 6 and 7 than bring x to one side. voila

2. anonymous

$\frac{ x }{ 6 }=\frac{ x }{ 7 }+5$ to better understand here is the actual problem in the correct equation

3. anonymous

Move the x's to one side. Make the denominators equal. Minus the two terms, and move the denominator over to the over side and multiply 5 by the denominator (42) and then divide by the number next to x on the side where 5(42) is. and voila

4. anonymous

7x/42 - 6x/42 = 5 x/42=5 x=5(42)

5. calculusfunctions

$\frac{ x }{ 6 }=\frac{ x }{ 7 }+5$ Multiply both sides by 42 (least common multiple of 6 and 7), to obtain 7x = 6x + 210 ∴ x = 210 Do you understand?

6. anonymous

so step 2 would look like x/7-x/6=5

7. anonymous

yes

8. anonymous

Then you make the denominators the same

9. anonymous

which would be 42,

10. anonymous

yes since 6 X 7 = 42

11. anonymous

this is the part i get confused at

12. anonymous

would it look like x/42?

13. anonymous

but in order to make the denominators equation, you need to times the numerator by the amount that the denominator needs to make 42. eg. 6 X ? = 42 (7) so times the top x by 7 which becomes 7x. and the other becomes 6x since you need to times 7 by 6 to make 42. so it would be 7x/42 - 6x/42 7x-6x = x so it will eventually become x/42

14. anonymous

ahhh ok

15. anonymous

so then is x/42=5

16. anonymous

Yup

17. anonymous

and then simplify from there

18. anonymous

yup :)

19. anonymous

how do i get x by itself?

20. anonymous

move the 42 over to the other side by timesing both sides by 42.

21. anonymous

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22. anonymous

42(x/42) = 5(42) x =210

23. anonymous

thank you so much.. fractions is one thing i have an issue with..

24. anonymous

that's fine :)

25. anonymous

i have even harder ones... like $\frac{ x}{ 2x+2 }=\frac{ -2x }{ 4x+4 }+\frac{ 2x-3 }{ x+1 }$

26. anonymous

You use the same principle: so to add two fractions, the denominators must be the same. make the denominator under -2x simplified: 4x + 4 4(x+1) and use {-2x over 4(x+1)} + {4(2x-3) over 4(x+1)} as a first step

27. anonymous

${-2x \over 4(x+1)} + {4(2x-3) \over 4(x+1)}$

28. anonymous

and add them $-2x + 8x -12 \over 4(x+1)$

29. anonymous

do the same with the other side and use 2(x+1) as denominator

30. anonymous

${x \over 2(x+1)} = {6x -12 \over 4(x+1)}$

31. anonymous

and cross multiply for simplification

32. anonymous

2x(x+1) = (6x-12) (x+1)

33. anonymous

cancel the x+1 and you have 2x = 6x-12

34. anonymous

and that is simplified as -4x = -12 which means x = 3

35. anonymous

understand?

36. anonymous

i believe so

37. anonymous

great :)

38. anonymous

i have one more fraction if anyone is interested in helping

39. anonymous

$\frac{ 5 }{ y-4 }-\frac{ 8 }{ y-4 }=\frac{ 2 }{ y^2-16 }$

40. anonymous

it throws me off to add sqrt

41. anonymous

um... you could do it like this: ${-3 \over y-4} = {2 \over y^2 -16}$ ${-3 \over y -4} = {2 \over (y+4)(y-4)}$

42. anonymous

Then knock off the y-4 so you're left with $-3 = {2 \over y+4}$

43. anonymous

and then use -3 (y+4) = 2 and simplify -3y - 12 = 2 -3y = 2 +12 -3y = 14 y = 14/-3

44. anonymous

y = -(14/3)

45. anonymous

wow that was easier than i thought

46. anonymous

You were only stumped by the y^2 - 16 which is simplified as (y-4)(y+4)

47. anonymous

thank you so much for helping me with these!

48. anonymous

No probelma :)