(x^3)(x-2)^(-3/2) + x(x-2)^(-1/2). okay so I tried to factor by grouping by taking out an x and (x-2) ^-3/2 from each side but it didn't really work, so I need help going from there or a different way to do it (like maybe temporary variables?).Thanks :)
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x^3(x - 2)^(-3/2) + x(x - 2)^(-1/2) =
x^3(x - 2)^(-3/2) + x(x - 2)(x - 2)^(-3/2) =
x^3(x - 2)^(-3/2) + (x^2 - 2x)(x - 2)^(-3/2) =
(x^3 + x^2 - 2x)(x - 2)^(-3/2) =
x(x^2 + x - 2)(x - 2)^(-3/2) =
x(x + 2)(x - 1)(x - 2)^(-3/2)
x^3(x - 2)^(-3/2) + x(x - 2)(x - 2)^(-3/2) =
x^3(x - 2)^(-3/2) + (x^2 - 2x)(x - 2)^(-3/2) =
(x^3 + x^2 - 2x)(x - 2)^(-3/2) =
x(x^2 + x - 2)(x - 2)^(-3/2) =
x(x + 2)(x - 1)(x - 2)^(-3/2)
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(x^3)(x - 2)^(-3/2) + x(x - 2)^(-1/2)
= (x^3)/[(x - 2)(3/2)] + x/(x - 2)^(1/2)
= [(x^3) + x(x - 2)] / (x - 2)^(1/2)
= (x^3 + x^2 - 2x) / (x/2)^(3/2)
= x(x^2 + x - 2) / (x/2)^(3/2)
= x(x - 1)(x + 2) / (x - 2)^(3/2)
= (x^3)/[(x - 2)(3/2)] + x/(x - 2)^(1/2)
= [(x^3) + x(x - 2)] / (x - 2)^(1/2)
= (x^3 + x^2 - 2x) / (x/2)^(3/2)
= x(x^2 + x - 2) / (x/2)^(3/2)
= x(x - 1)(x + 2) / (x - 2)^(3/2)