• Jan 5th 2010, 02:37 AM
want2math
I'm doing some algebraic mistake because I think my method is right.

The question is to find the gradient of $\displaystyle (p+q-1, q+p-3)(p-q+1, q-p+3)$

My attempt for the question is.

$\displaystyle \frac{(q-p+3)-(q+p-3)}{(p-q+1)-(p+q-1)}$

$\displaystyle \frac{q-p+3-q-p+3}{p-q+1-p-q+1}$

$\displaystyle \frac{-2p+6}{-2q+2}$

$\displaystyle \frac{2p+3}{2q+1}$

$\displaystyle ans = \frac{p+3}{q}$

But the answer on the book is different. :(
• Jan 5th 2010, 02:40 AM
earboth
Quote:

Originally Posted by want2math
I'm doing some algebraic mistake because I think my method is right.

The question is to find the gradient of $\displaystyle (p+q-1, q+p-3)(p-q+1, q-p+3)$

My attempt for the question is.

$\displaystyle \frac{(q-p+3)-(q+p-3)}{(p-q+1)-(p+q-1)}$

$\displaystyle \frac{q-p+3-q-p+3}{p-q+1-p-q+1}$

$\displaystyle \frac{-2p+6}{-2q+2}$ <<<<<< I'll take this term.

$\displaystyle \frac{2p+3}{2q+1}$

$\displaystyle ans = \frac{p+3}{q}$

But the answer on the book is different. :(

$\displaystyle \frac{-2p+6}{-2q+2} = \frac{-2(p-3)}{-2(q-1)}$

Cancel the common factor.
• Jan 5th 2010, 02:41 AM
Prove It
Quote:

Originally Posted by want2math
I'm doing some algebraic mistake because I think my method is right.

The question is to find the gradient of $\displaystyle (p+q-1, q+p-3)(p-q+1, q-p+3)$

My attempt for the question is.

$\displaystyle \frac{(q-p+3)-(q+p-3)}{(p-q+1)-(p+q-1)}$

$\displaystyle \frac{q-p+3-q-p+3}{p-q+1-p-q+1}$

$\displaystyle \frac{-2p+6}{-2q+2}$

You are correct up to here.

Now factorise:

$\displaystyle \frac{-2(p - 3)}{-2(q - 1)}$

Cancel out the common factor:

$\displaystyle \frac{p - 3}{q - 1}$.
• Jan 5th 2010, 02:42 AM
want2math
Quote:

Originally Posted by Prove It
You are correct up to here.

Now factorise:

$\displaystyle \frac{-2(p - 3)}{-2(q - 1)}$

Cancel out the common factor:

$\displaystyle \frac{p - 3}{q - 1}$.

Awesome, thanks to both of you.