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Math Help - Complex Gradient Question

  1. #1
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    Complex Gradient Question

    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.
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  2. #2
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    Quote Originally Posted by want2math View Post
    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.
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  3. #3
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    Quote Originally Posted by want2math View Post
    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}.
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  4. #4
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    Quote Originally Posted by Prove It View Post
    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.
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