Question

3/m-4 + 1/3(m-4) = 6/m
The only other info it gives says: You can solve a rational equation by multiplying each side by the LCD. Check possible solutions to make sure each satisfies the original equation.

Answer 1

\[\large \frac{3}{m - 4} + \frac{1}{3}(m - 4) = \frac{6}{m}\]

Like that right?

Answer 2

Or is it

\[\large \frac{3}{m - 4} + \frac{1}{3(m - 4)} = \frac{6}{m}\]

Answer 3

Ehh for simplicity I believe it would be the second one I posted...

So what is the LCD for that one? Well if you see...the only difference between the 2 denominators....is the second one is the first one..just multiplied by 3....so lets multiply the whole first fraction by 3/3 to even that out...

\[\large \frac{3}{3} \times \frac{3}{(m - 4)} + \frac{1}{3(m - 4)} = \frac{6}{m}\]
\[\large \frac{9}{\color \red{3(m - 4)}} + \frac{1}{\color \red{3(m - 4)}} = \frac{6}{m}\]
Now we have a common denominator ...so lets combine those 2 fractions over that common denominator

\[\large \frac{9 + 1}{3(m - 4)} = \frac{6}{m}\]
\[\large \frac{10}{3(m - 4)} = \frac{6}{m}\]

Lets cross multiply here

\[\large 10m = 6 \times 3(m - 4)\]
\[\large 10m = 18(m - 4)\]

Can you go from there?

Answer 4

@DollyAcquah he is offline, could you help me finish this?

Answer 5

sorry to far ahead of me im in 8th grade

Answer 6

@natedog12 @secret66 @Luigi0210 @ShaTay @YanaSidlinskiy

Answer 7

@wyattp17

Answer 8

do you have any answer choices?

Answer 9

Does @johnweldon1993 not help you?? I promise...He will get you through it...

Answer 10

not me

Answer 11

i have the answer i just need to show my work

Answer 12

he is not online anymore! but he was helping alot!

Answer 13

the answer is 9 but i need to show my work, and i dont know how to do this question

Answer 14

Trust me...Either message or email him..

Answer 15

well if he is offline he isnt going to get it until he comes back online.. but i wanted to get this done soon. I just needed to know how to show the work for it. @geniousmind13 the answer is 9, do you know the work to show for that?

Answer 16

yes just a minute and i will have it posted

Answer 17

thank you :)

Answer 18

here it is hope it helps

Answer 19

@Reilly208 still online??

Answer 20

Well I'm wondering if you understood everything I have done so far...

Answer 21

hi john gues what

Answer 22

If so...

we stopped after cross multiplying and now we have

\[\large 10m = 18(m - 4)\]

Distribute that 18 into the parenthesis

\[\large 10m = 18m - 72\]

Combine like terms...subtract 18m from both sides of this equation

\[\large -8m = -72\]

And finally just divide both sides by -8

\[\large m = 9\]

Answer 23

what? @natedog12

Answer 24

my dad names is john