Question

solve for x : equation inside

Answer 1

\[\frac{ 3 }{ x + 2 } - \frac{ 1 }{ x } = \frac{ 1 }{ 5x }\]

Answer 2

phi: this is my last question of the night. hahaha :)

Answer 3

bring 1/5x to the left side
find a common denominator

Answer 4

i guess x is the common denominator?

Answer 5

\[\frac{ 3 }{ x + 2 } - \frac{ 1 }{ x } - \frac{ 1 }{ 5x } = 0\]

Answer 6

this is an equality, so not as tricky.

another way to do this is multiply both sides (and all terms) by (x+2)
and then by 5x
(this "clears" the denominators)

can you do that ?

Answer 7

how would that clear the middle denominator?

Answer 8

one step at at time. what do you get if you multiply all terms and both sides of the equation by (x+2) ?

Answer 9

i have no idea.

Answer 10

if you show me what it looks like when you multiply all the terms by (x + 2) i will do it and then try it myself with 5x

Answer 11

just write (x+2) next to each term

Answer 12

and remember you can simplify (x+2)/(x+2) to 1

Answer 13

\[3 - \frac{ 1 }{ x ( x + 2) } - \frac{ 1 }{ 5x ( x + 2) } = (x + 2)\]

Answer 14

actually its all equal to 0. dumb error in my fault

Answer 15

yes, and you should by multiplying by (x+2). that means (x+2) goes in the "top"

you divided by (x+2) (except for the first term, which you did correctly)

Answer 16

\[3 - \frac{ x + 2 }{ x } - \frac{ x + 2 }{ 5x } = 0\]

Answer 17

now multiply all terms, both sides by 5x. write 5x (in the top) next to each term

Answer 18

\[3(5x) - \frac{ 5x ( x + 2) }{ x } - 1 = 0\]

Answer 19

the last term is not -1. just put 5x next to the last term.

Answer 20

my mistake.

\[3(5x) - \frac{ 5x ( x + 2 }{ x } + 5x = 0\]

Answer 21

is that right?

Answer 22

5x times the last term. not just 5x

Answer 23

\[3 ( 5x) - \frac{ 5x ( x + 2) }{ x } - \frac{ 5x }{ 5x} = 0 \]

Answer 24

???

Answer 25

\[ 3(5x) - \frac{ 5x(x + 2) }{ x } - \frac{ 5x(x + 2) }{ 5x } = 0(5x) \]
now simplify. If you have the samething in the top and bottom, you can cancel them

Answer 26

what do i do with \[\frac{ 5x ( x + 2) }{ x }\]

Answer 27

the x in the top and bottom cancel, because x/x = 1

Answer 28

so then i get 10x?

Answer 29

\[15x - 10x - x + 2 = 0\]

Answer 30

15x is ok
\[ 3(5x) - \frac{ 5\cancel{x}(x + 2) }{ \cancel{x} } - \frac{ \cancel{5x}(x + 2) }{ \cancel{5x} } = 0(5x) \\
15x - 5(x+2) -(x+2) = 0 \]
can you finish ?

Answer 31

yes

Answer 32

9x = -12

Answer 33

x = -12/9

Answer 34

correct?

Answer 35

actually x = 12/9

Answer 36

what do you get when you distribute the -5 in
-5(x+2)
?
you should get -5 times each term

Answer 37

yeah, -5x + -10

Answer 38

15x - 5x - 10 - x - 2 = 0
9x - 12 = 0
9x = 12
x = 12/9

Answer 39

you can simplify. top and bottom can be divided by 3

Answer 40

x = 4/3