# Simple Algebra...

• Oct 28th 2008, 05:55 PM
BCHurricane89
Simple Algebra...
I feel really stupid asking this question, but im trying to help a friend do this problem, yet I dont know how to do it. I am sure it is something easy, and maybe if I saw it, it would click, but right now, im stumped.

solve for m

$\displaystyle \frac {2}{m+1} = \frac {3}{2m+3}$

first, I tried splitting them up, like so:

$\displaystyle \frac {2}{m} +2 = \frac {3}{2m} +1$

$\displaystyle \frac {2}{m} = \frac {3}{2m} -1$
• Oct 28th 2008, 06:01 PM
Jhevon
Quote:

Originally Posted by BCHurricane89
I feel really stupid asking this question, but im trying to help a friend do this problem, yet I dont know how to do it. I am sure it is something easy, and maybe if I saw it, it would click, but right now, im stumped.

solve for m

$\displaystyle \frac {2}{m+1} = \frac {3}{2m+3}$

first, I tried splitting them up, like so:

$\displaystyle \frac {2}{m} +2 = \frac {3}{2m} +1$

$\displaystyle \frac {2}{m} = \frac {3}{2m} -1$

you cannot split fractions like that!

anyway, multiply the equation through by the LCD of the denominators, namely (m + 1)(2m + 3). now continue

and remember, in general, $\displaystyle \frac a{b + c} \ne \frac ab + \frac ac$. never make that mistake again
• Oct 28th 2008, 06:06 PM
BCHurricane89
wow, I could've sworn you could split the fraction like that, I swear we did that before...hmm, oh wait nvm...thats when we had like

$\displaystyle \frac {2m+2}{3}$ then we could split it
• Oct 28th 2008, 06:10 PM
Jhevon
Quote:

Originally Posted by BCHurricane89
wow, I could've sworn you could split the fraction like that, I swear we did that before...hmm, oh wait nvm...thats when we had like

$\displaystyle \frac {2m+2}{3}$ then we could split it

yes, this can be split into $\displaystyle \frac {2m}3 + \frac 23$

the denominator has to stay intact. you may separate the terms of the numerator, but make sure you put each over the whole denominator.
• Oct 28th 2008, 06:12 PM
Rafael Almeida
Quote:

Originally Posted by BCHurricane89
wow, I could've sworn you could split the fraction like that, I swear we did that before...hmm, oh wait nvm...thats when we had like

$\displaystyle \frac {2m+2}{3}$ then we could split it

Exactly, you can split when the numerator is a sum. This because taking the GCD of the two new denominators and joining back the fractions lead you to the same place you started.

However, this is not true with denominators. There's the Partial Fractions method to deal with them, but you usually don't need them in this context.