Question

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6. (1 over 3x - 2) + (5 over x) = 0

Answer 1

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

Answer 2

First you need to make the fractions have the same denominator:
\[\frac{ x }{ x(3x -2) } + \frac{ 5(3x - 2) }{ x(3x-2) } = 0\]
Then just add the fractions together (x + 5(3x - 2) becomes the numerator) and simplify the numerator. From there, you know that the numerator will equal zero if the entire expression equals zero.

Answer 3

^What he saidm and here are a few values x cannot have, x=0, and x=2/3. This is so because at these values, the function will be non existent. (case being of denominator=0)

Answer 4

so @Fruitbasket will it be 5x(3x - 2) = 0

Answer 5

^No, what he said, si the quation is x+15x-10=0
That is 16x=10 i.e. x=5/8

Answer 6

To which I added the two values x cannot have and the reason for me stating so.

Answer 7

I need help not a lecture, did I do it right

Answer 8

No. The "lecture" was just a solution in detail to make it clear.

Answer 9

I think its
x
-------
15x - 10

Answer 10

which goes 15x - 10x

but im not 100%

Answer 11

How did you get that

Answer 12

15x^2 - 10

Answer 13

15x-10 =5x

5x=0
- -
5 5
x=0

Answer 14

I think its
x
------- =0 multiply 1x to everything
15x - 10

15x - 10x =0 now combine like terms

5x=0 now get the variable by its self by dividing 5
- -
5 5
x=0 which gives you X = 0

Answer 15

if I helped and its correct give a best answer for people to know hehe was I any help

Answer 16

do you understand what I put

Answer 17

@michaelc96 should it be 15x^2 - 10x

Answer 18

5x(3x - 2) = 0
divide by 5
x( 3x - 2) = 0
Split into 2 problems
x = 0 or 3x - 2 = 0 <--- x = 2/3

Answer 19

right?

Answer 20

so your saying should 15x be to the second power

Answer 21

yes

Answer 22

I would say yes imam see if @Mertsj can help

Answer 23

the answer should be x = 5/8

Answer 24

Right away, before we do anything, we see that x cannot be 2/3 or 0
Now we can go ahead and write both fractions with the common denominator x(3x-2)

Answer 25

Well actually, I didn't see that it was an equation so we should just multiply every term on both sides by the common denominator. This will eliminate all denominators and we will end up with:

Answer 26

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

Answer 27

Which, cancelling common factors gives us:
\[x+5(3x-2)=0\]

Answer 28

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

Answer 29

\[16x-10=0\]

Answer 30

\[16x=10\]

Answer 31

\[x=\frac{10}{16}=\frac{5}{8}\]

Answer 32

man you know your stuff hehe

Answer 33

that's why I refer to him! :D

Answer 34

ty

Answer 35

pfft yet I was the on to call him im guessing your always in this part

Answer 36

Whatever, dude

Answer 37

Just so the problem got solved. Everyone's happy, right?

Answer 38

yup

Answer 39

yep