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Math Help - Algebraic fraction help please.

  1. #1
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    Algebraic fraction help please.

    Write as a single fraction and simplify,
    (8/ x^2 + 2x -3) - (4/ x^2 - 1)
    Can someone help me with this q please? Thanks
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  2. #2
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    Quote Originally Posted by Detanon View Post
    Write as a single fraction and simplify,
    (8/ x^2 + 2x -3) - (4/ x^2 - 1)
    Can someone help me with this q please? Thanks
    1. Factorize the denominators:

    \dfrac8{x^2+2x-3} - \dfrac4{x^2-1} = \dfrac8{(x-1)(x+3)} - \dfrac4{(x-1)(x+1)}

    2. The general denominator is (x-1)(x+1)(x+3).

    3. Therefore the difference becomes:

    \dfrac{8(x+1)}{(x-1)(x+1)(x+3)} - \dfrac{4(x+3)}{(x-1)(x+1)(x+3)}

    4. Expand the numerators and collect like terms.

    \dfrac{8x+8 - 4x-12}{(x-1)(x+1)(x+3)} = \dfrac{4(x-1)}{(x-1)(x+1)(x+3)}

    Now cancel:

    \dfrac{4}{(x+1)(x+3)}\ ,\ x \neq 1
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