# Thread: I need some clarification

1. ## I need some clarification

my prof did this in his lecture:

$\displaystyle \frac{A(x-1)+B(x+2)}{(x+2)(x-1)}$

= $\displaystyle \frac{x(A+B)+2(A-B)}{(x+2)(x-1)}$

Can anyone tell me what he did?

2. Originally Posted by jschlarb
my prof did this in his lecture:

$\displaystyle \frac{A(x-1)+B(x+2)}{(x+2)(x-1)}$

= $\displaystyle \frac{x(A+B)+2(A-B)}{(x+2)(x-1)}$

Can anyone tell me what he did?
$\displaystyle \frac{A(x-1)+B(x+2)}{(x+2)(x-1)}=\frac{Ax-A+Bx+2B}{(x+2)(x-1)}= \frac{Ax+Bx+2B-A}{(x+2)(x-1)}$

= $\displaystyle \frac{x(A+B)+(-A+2B)}{(x+2)(x-1)}$

I don't think that they are equal

3. Hi again

Originally Posted by jschlarb
my prof did this in his lecture:

$\displaystyle \frac{A(x-1)+B(x+2)}{(x+2)(x-1)}$
$\displaystyle =\frac{Ax-A+Bx+2B}{(x+2)(x-1)}$, by expanding.

$\displaystyle =\frac{Ax+Bx-A+2B}{(x+2)(x-1)}$, by rearranging.

= $\displaystyle \frac{x(A+B)+({\color{red}2B-A})}{(x+2)(x-1)}$

Can anyone tell me what he did?
There's something wrong in what you've written ~

4. Originally Posted by jschlarb
my prof did this in his lecture:

$\displaystyle \frac{A(x-1)+B(x+2)}{(x+2)(x-1)}$

= $\displaystyle \frac{x(A+B)+2(A-B)}{(x+2)(x-1)}$

Can anyone tell me what he did?
$\displaystyle \frac{Ax-A+Bx+2B}{(x+2)(x-1)}$

$\displaystyle \frac{Ax+Bx+2B - A}{(x+2)(x-1)}$

$\displaystyle \frac{x(A+B)+ (2B - A)}{(x+2)(x-1)}$

That's as far as I get though...

5. Originally Posted by Moo
Hi again

$\displaystyle =\frac{Ax-A+Bx+2B}{(x+2)(x-1)}$, by expanding.

$\displaystyle =\frac{Ax+Bx-A+2B}{(x+2)(x-1)}$, by rearranging.

There's something wrong in what you've written ~

That makes MUCH more sense. Thanks!