Question

Equation Below
Fan and a Medal!!(:

Answer 1

\[-\frac{ z-2 }{ 10z-15 }=\frac{ 1 }{ 2z-3 }-\frac{ 6 }{ 2x-3 }\]

Answer 2

@mathmale

Answer 3

Hello! What kind of help do you need? I see that one of your denominators ix 2z-3 and another is 2x-3. Is that correct?

Answer 4

Sorry @mathmale they are all x's

Answer 5

that was a typo

Answer 6

Please check this over and see if it exactly reproduces the problem printed in your materials.

\[-\frac{ x-2 }{ 10x-15 }=\frac{ 1 }{ 2x-3 }-\frac{ 6 }{ 2x-3 }\]

Answer 7

dang.. it I meant they are all z's,
I am having a tough time right now focusing well..
But yes that is correct but with all z's @mathmale

Answer 8

Let's stay with all x's so long as the equation is correct otherwise.

Answer 9

All right!!

Answer 10

Please express in y our own words what the instructions for this problem say.

Answer 11

I thought this would be not possible because they all have the same letter variable.. @mathmale

Answer 12

Let's go with the flow; I think you'll see that there are now no obstacles. But again, what is your objective here? What are you supposed to do?

Answer 13

I am supposed to solve for z(in this case x) @mathmale

Answer 14

Just change that to, "I am supposed to solve for x." ;)

take a good, hard look at the 3 denominators. Do they seem to have anything in common? If so, explain what they have in common.

Answer 15

I am supposed to solve for x.

They can all be multiplied by 2 numbers? @mathmale

Answer 16

Could you please be a bit more specific?: Why multiply some or all of the denominators "by 2 numbers"? First, name your objective. Why would we want to multiply any of the den. by something else? Note: you are not wrong...I just want more specifics.

Answer 17

What's a general rule for combining fractions, by the way?

Answer 18

I really don't know :(
I am very bad at math and I am really hard on myself about it... I am trying to learn but I just don't know @mathmale

Answer 19

Look at the denominators of the middle and right fractions. They're the same, correct?

Answer 20

Correct @mathmale

Answer 21

Look at the denom. of the leftmost fraction. Could it be factored? If so, what are the factors?

Answer 22

5x-3? @mathmale

Answer 23

Hint: Is there any way in which you could factor this denominator so that one of the factors is the same as the factor of the right two fractions?

Answer 24

sorry! I meant 2x-3!
I divided by 5 then had the number 5 stuck in my mind :D @mathmale

Answer 25

So, your first den. (denominator) is 5(2x-3). The 5 is unique to that den.; the other two dens. don't have it as a factor.

To combine these fractions, or to eliminate the dens. altogether, we need to have exactly the same den. in each fraction. How would you accomplish that?

Answer 26

would you combine the numbers that have the x's?
@mathmale

Answer 27

Let's copy down the equation as it now stands:

}\[-\frac{ x-2 }{ 10x-15 }=\frac{ 1 }{ 2x-3 }-\frac{ 6 }{ 2x-3 }\]

Answer 28

As you said, we can factor 5 out of the denom. 10x-15, resulting in our having 5(2x-3).
We could have all the dens. the same if we'd multiply both numerator and denominator of the 2 rightmost fractions by 5. Would y ou please try that?

Answer 29

If you've done this correctly, all of your fractions will have the same den.

Answer 30

I will be done for about 2 minutes. Continue working on this problem, please.

Answer 31

I will continue! @mathmale

Answer 32

don't spend a lot of time on this. All you really have to do is to put parentheses around each numerator in the 2nd 2 fractions and the same around each den., and then multiply both num. and den. by 5. That's it. Don't multiply beyond that, at least not yet.

Answer 33

How are you doing on this work?

Answer 34

@sophadof?

Answer 35

It's confusing me... @mathmale sorry i took so long to respond

Answer 36

so then all the denominators look like this?
5(2x-3) @mathmale

Answer 37

Indeed they do. What are the new numerators for the right 2 fractions?

Answer 38

That would be...

Answer 39

5 and 30? @mathmale

Answer 40

After multiplying numerator and den. of both of the right two fractions by 5, we should have:\[-\frac{ x-2 }{ 10x-15 }=\frac{5* 1 }{5*( 2x-3) }-\frac{5* 6 }{5( 2x-3) }\]

Answer 41

Yes, 5 and 30. Very good.

Answer 42

Now, since all of the dens. are the same, we can simply cross out the dens. This leaves us with the numerators only, in the following equation:

-(x-2)=5-30

Answer 43

Please simplify this, and solve for x.

Answer 44

\[-\frac{ x-2 }{ 10x-15 }=\frac{ 5*1 }{5( 2x-3) }-\frac{5( 6) }{5( 2x-3) }\]

Answer 45

27!? @mathmale

Answer 46

that looks good! Ideally, you'd check your result, x=27, to ensure that it truly does make the given equation true.

Answer 47

OH MY GOSH! THANK YOU SO SO SO MUCH! (: @mathmale

Answer 48

If yes, then x=27 or z=27 is your solution.

My great pleasure to work with you! See you again.