## misswiss123 2 years ago Solve the equation: 2/5 - 3/x = 1/(5x)

1. gaara438125

$\frac{ 2 }{ 5 } - \frac{ 3 }{ x } = \frac{ 1 }{ 5x }$ what's the LCD?

2. misswiss123

I don't know

3. gaara438125

$\frac{ 2 }{ 3 } +\frac{ 7 }{ x } + \frac{ 32 }{ 6x }$ the LCD would be 6x for all the denominators can multiply into 6x 3 * 2x | x * 6 | 6x * 1 |

4. gaara438125

what ever you multiply the denominator by you HAVE to multiply the same number to the numerator.

5. misswiss123

x=8 ?

6. gaara438125

let's go back to the original equation and look at that in the denominator what is the highest number they can all equal? 5, x, and 5x

7. gaara438125

lowest number*

8. misswiss123

1?

9. gaara438125

touche -.-" lol i meant without dividing 5, x and 5x can ALL equal 5x

10. misswiss123

I have no idea ;'(

11. jim_thompson5910

2/5 is equivalent to (2x)/(5x) if you multiply top and bottom by x -3/x is equivalent to 15/(5x) if you multiply top and bottom by 5 Notice how they now have the same denominator of 5x This means 2/5 - 3/x = 1/(5x) is the same as (2x)/(5x) - 15/(5x) = 1/(5x) which allows you to combine the two fractions on the left side to get (2x - 15)/(5x) = 1/(5x) What's next?

12. jim_thompson5910

any ideas?

13. misswiss123

aaahhhhhh

14. jim_thompson5910

yes? no?

15. jim_thompson5910

If two fractions are equal, and their denominators are equal, then the numerators must be equal

16. jim_thompson5910

so this means that if (2x - 15)/(5x) = 1/(5x) then 2x-15 = 1

17. jim_thompson5910

if 2x - 15 = 1, then x = ???

18. misswiss123

8?

19. jim_thompson5910

you got it

20. misswiss123

Thank youu

21. jim_thompson5910

yw