ratnl eqns different denominators: 2x-4/24x + -2x+4/-24x

[anm2007]

how do i solve this rational equation with ddiffernt denominators?

2x-4/24x + -2x+4/-24x

 

[o_O]

Do you mean:
\(\displaystyle \frac{2x-4}{24x} + \frac{-2x + 4}{-24x}\)

Well there's nothing to solve for since there is no equation to start with but if you mean to simplify, why don't you factor out a -1 from the second fraction there?

 

[anm2007]

Do you mean:
\(\displaystyle \frac{2x-4}{24x} + \frac{-2x + 4}{-24x}\)

Well there's nothing to solve for since there is no equation to start with but if you mean to simplify, why don't you factor out a -1 from the second fraction there?

yes i did that but im not sure i did that right. could u show me how to exactly do that?

 

[o_O]

\(\displaystyle \frac{2x-4}{24x} + \frac{-1(2x-4)}{-1(24x)}\)

See what the point of factoring out the -1 was? Then add your fractions accordingly.

 

[anm2007]

\(\displaystyle \frac{2x-4}{24x} + \frac{-1(2x-4)}{-1(24x)}\)

See what the point of factoring out the -1 was? Then add your fractions accordingly.

no actually i dont see the point because it is still -2x+4 / -24x isnt it?

 

[o_O]

What cancels out?

 

[anm2007]

What cancels out?

umm...the 2x-4 and the 24x's? i dont get it? does taht mean the answer is 0?

 

[o_O]

No it doesn't. See how I factored out the -1 from both the top and bottom in the second fraction? Doesn't that mean I can cancel them out?

If I had something like:
\(\displaystyle \frac{ax+ba}{ac}\)

I could factor out the 'a' and they would cancel:
\(\displaystyle \frac{a(x + b)}{a(c)} = \frac{x + b}{c}\)

Same principle.

 

[anm2007]

No it doesn't. See how I factored out the -1 from both the top and bottom in the second fraction? Doesn't that mean I can cancel them out?

If I had something like:
\(\displaystyle \frac{ax+ba}{ac}\)

I could factor out the 'a' and they would cancel:
\(\displaystyle \frac{a(x + b)}{a(c)} = \frac{x + b}{c}\)

Same principle.

ok so that means that now the problem look like this:

2x-4/24x + -2x+4/24x?

 

[anm2007]

No it doesn't. See how I factored out the -1 from both the top and bottom in the second fraction? Doesn't that mean I can cancel them out?

If I had something like:
\(\displaystyle \frac{ax+ba}{ac}\)

I could factor out the 'a' and they would cancel:
\(\displaystyle \frac{a(x + b)}{a(c)} = \frac{x + b}{c}\)

Same principle.

ok so that means that now the problem look like this:

2x-4/24x + -2x+4/24x?

no thats not right.....IM SOO CONFUSED!

 

[o_O]

Not quite. This is what i wrote:
\(\displaystyle \frac{2x-4}{24x} + \frac{-1(2x-4)}{-1(24x)}\)

If I cancel the -1's in the second fraction, the top and bottom remains the same: so it'll be \(\displaystyle \frac{2x - 4}{24x}\) NOT \(\displaystyle \frac{-2x + 4}{24x}\). Now that you have a common denominator, you can add the numerators.

Also, you have a common factor that you can cancel in both top and bottom when you add the two fractions together. Keep that in mind after you do the adding.

 

[anm2007]

Not quite. This is what i wrote:
\(\displaystyle \frac{2x-4}{24x} + \frac{-1(2x-4)}{-1(24x)}\)

If I cancel the -1's in the second fraction, the top and bottom remains the same: so it'll be \(\displaystyle \frac{2x - 4}{24x}\) NOT \(\displaystyle \frac{-2x + 4}{24x}\). Now that you have a common denominator, you can add the numerators.

Also, you have a common factor that you can cancel in both top and bottom when you add the two fractions together. Keep that in mind after you do the adding.

so now when i add the numerators i get 4x+8 / 24x right?

 

[o_O]

Not quite. Looking at the numerator. What's 2x - 4 + 2x - 4. More specifically what's -4 + -4?

Also, what's a common factor you can take out from both top and bottom?

Anyway, I'm actually going to go now. Good luck!

 

[anm2007]

Not quite. Looking at the numerator. What's 2x - 4 + 2x - 4. More specifically what's -4 + -4?

Also, what's a common factor you can take out from both top and bottom?

Anyway, I'm actually going to go now. Good luck!

ooo 4x-8 / 24x?

 

[Denis]

4x-8 / 24x?

Yes; but PLEASE start using BRACKETS when necessary: (4x - 8) / 24x

You can now simplify a bit this way:
4(x - 2) / [4(6x)] ; cancel the 4's:
(x - 2) / (6x)
Got it?

 

[stapel]

IM SOO CONFUSED!

It's looking like you're quite lost. You might want to take a break from specific exercises, and try studying some online lessons first...? :idea:

Once you get a better grasp of the material, the replies you've received should make more sense, and you should be able to make better progress!

Eliz.