math calculus

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7/(x-2)(x+5)-8/(x+5)(x-3)

7(x-3)-8(x-2)/(x-2)(x+5)(x-3)

7x-21-8x+16/(x-2)(x+5)(x-3)

7x-8x give me -1x and -21+16 give me -5. for numerator but it have to be -1/(x-2)(x-3)

i not know how to do this please explain process my way not different way.

  • math calculus -

    You have to use brackets to show that both
    x-2 and x+5 are factors of the bottom, so ...
    7/((x-2)(x+5)) - 8/((x+5)(x-3)

    so the lowest common denominator is (x-2)(x+5)(x-3)
    we get
    [ 7(x-3) - 8(x-2) ] /[(x-2)(x+5)(x-3)]
    = [7x - 21 - 8x + 16]/[(x-2)(x+5)(x-3)]
    = (-x - 5)/[(x-2)(x+5)(x-3)]
    = -1(x+5)/[(x-2)(x+5)(x-3)]
    = -1/[(x-2)(x-3)]

  • math calculus -

    = (-x - 5)/[(x-2)(x+5)(x-3)]
    i understand how u do this part


    = -1(x+5)/[(x-2)(x+5)(x-3)]
    i not understand how you get numerator

  • math calculus -

    I simply factored out a -1

  • math calculus -

    sorry but that the only thing i don't understand how do u factor that out? could you please explains slowly

  • math calculus -

    suppose you had

    2x + 4
    then it would be 2(x+2)

    suppose you had
    -2x - 4
    then it would be -2(x+2)

    suppose you had -x -5
    then it would be -1(x+5)

    in each case, expand my answer and see what you get.

  • math calculus -

    thank you very much reiny for taking time to explain :) u took all confusion away :)

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