Adding Fractions in Algebra

Date: 2/9/96 at 21:53:5
From: Jason Lee
Subject: Addition of fractions (monomial by binomial)

Here's the problem :

2a + b   a
------ + -
 a - b   b

Here's what I did, though I don't think it's right. There's probably an
easier way.

Cross multiply. And multiply the denominators.
And I get :

2a + b^2    a^2 - b   2a + b^2 + a^2 - b
-------- +  ------- = ------------------ ????
 a - b^2    a - b^2        a - b^2

And can I simplify if it is correct?

Date: 2/14/96 at 18:11:16
From: Doctor Byron
Subject: Re: Addition of fractions (monomial by binomial)

Hi, Jason.  You seem to understand the basics of how to do this kind
of problem well.  In fact there is only a small error in your method.
If you'll look further down in your letter, I'll point it out.

>2a + b^2    a^2 - b   2a + b^2 + a^2 - b
>-------- +  ------- = ------------------ ????
> a - b^2    a - b^2        a - b^2
  |
  |---Right here, you forgot to distribute the b to both terms
when multiplying the denominators.  Therefore, ab - b^2 should be
the denominator in both cases.  You also missed a similar 
distribution in the first numerator.  You seem to have the idea 
of the method, however.  And don't worry, even math doctors make those
kind of mistakes.

-Doctor Byron,  The Math Forum