# How did this happen?

• Apr 13th 2010, 08:51 PM
stills
How did this happen?
This solution comes from a differential calculus book. It seems to be on the simplifying stage already since it involves algebra. I'm wondering how it goes that way. Hopefully someone can explain this to me. Thanks!

http://i761.photobucket.com/albums/xx258/ws360/math.jpg
• Apr 13th 2010, 08:55 PM
harish21
Quote:

Originally Posted by stills
This solution comes from a differential calculus book. It seems to be on the simplifying stage already since it involves algebra. I'm wondering how it goes that way. Hopefully someone can explain this to me. Thanks!

http://i761.photobucket.com/albums/xx258/ws360/math.jpg

$x(x+1)^2$ is a common factor of both the terms.

Try viewing the term as:

$3(a^2)(b^2)+2ab^3$

this can be expressed as:

$ab^2 [ 3a + 2b]$

where:

$a= x$ and $b = x+1$
• Apr 13th 2010, 09:19 PM
stills
oops,
forget to notice the common factor.
thanks bro:D
I would like to add another question,
what if, of different exponent?
like this one:

X^4 (x^2-a^2)^-1/2 + 3x^2 (x^2-a^2)^1/2
• Apr 13th 2010, 09:27 PM
harish21
Quote:

Originally Posted by stills
oops,
forget to notice the common factor.
thanks bro:D
I would like to add another question,
what if, of different exponent?
like this one:

X^4 (x^2-a^2)^-1/2 + 3x^2 (x^2-a^2)^1/2

that would be:

$\frac{x^4}{\sqrt{(x^2-a^2)}} + 3x^2 \sqrt{(x^2-a^2)}$

Can you simplify this?
• Apr 14th 2010, 01:02 AM
mr fantastic
Quote:

Originally Posted by stills
This solution comes from a differential calculus book. It seems to be on the simplifying stage already since it involves algebra. I'm wondering how it goes that way. Hopefully someone can explain this to me. Thanks!

http://i761.photobucket.com/albums/xx258/ws360/math.jpg

It has been factorised by taking out the common factor of $x(x + 1)^2$.