Dividing Rational Expressions

Question

Answer 1

[(x^2 - 9x - 10)/(x^2  + x - 6)] / [(x^2 - 1)/ (x^2 - 4)]

     =   [(x^2 - 9x - 10)/(x^2  + x - 6)] X [(x^2 - 2^2)/ (x^2 - 1^2)]

    =   [(x^2  + x - 10x - 10)/(x^2  + 3x - 2x - 6)] X [(x + 2)(x - 2)/(x + 1)(x - 1)]

     =   [x(x  + 1)-10(x + 1)/(x(x + 3 )-2(x + 3)] X [(x + 2)(x - 2)/(x + 1)(x - 1)]

     =   [(x  + 1)(x - 10)/(x + 3 )(x - 2)] X [(x + 2)(x - 2)/(x + 1)(x - 1)]

     =   [(x - 10)(x + 2)] / [(x + 3 )(x - 1)]

Hence,

[(x^2 - 9x - 10)/(x^2  + x - 6)] / [(x^2 - 1)/ (x^2 - 4)]    =   [(x - 10)(x + 2)] / [(x + 3 )(x - 1)]