I'm doing some algebraic mistake because I think my method is right.

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

My attempt for the question is.

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

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

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

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

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

But the answer on the book is different.

2. 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 $(p+q-1, q+p-3)(p-q+1, q-p+3)$

My attempt for the question is.

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

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

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

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

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

But the answer on the book is different.
$\frac{-2p+6}{-2q+2} = \frac{-2(p-3)}{-2(q-1)}$

Cancel the common factor.

3. 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 $(p+q-1, q+p-3)(p-q+1, q-p+3)$

My attempt for the question is.

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

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

$\frac{-2p+6}{-2q+2}$
You are correct up to here.

Now factorise:

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

Cancel out the common factor:

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

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

Now factorise:

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

Cancel out the common factor:

$\frac{p - 3}{q - 1}$.
Awesome, thanks to both of you.