How do you simplify $x^(3/2)((x+x^5)/(2-x^2))$ ?

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Answer 1 · 2018-01-14T18:02:38

$(x^(3/2)(x+x^5))/(2-x^2)$ , or $(x^(5/2)(1+x^4))/(2-x^2)$

$x^(3/2)((x+x^5)/(2-x^2))$

$x^(3/2) = x^3 * x^(1/2)$

$x^(1/2) = sqrtx -> x^(3/2) = sqrt(x^3)$ or $xsqrtx$

$x^(3/2) * ((x+x^5)/(2-x^2)) = (x^(3/2)(x+x^5))/(2-x^2)$

$x^(3/2)(x+x^5) = (x^(3/2)* x^1) + (x^(3/2) * x^5)$

$x^(3/2)* x^1 = x^(3/2 + 1) = x^(5/2)$
$x^(3/2) * x^5 = x^(3/2 + 5) = x^(13/2)$

$(x^(3/2)(x+x^5))/(2-x^2) = (x^(5/2) + x^(13/2))/(2-x^2)$

$x^(5/2) + x^(13/2) = x^(5/2) (1+x^(8/2))$
$= x^(5/2)(1+x^4)$

the expression cannot be simplified further, so is either $(x^(3/2)(x+x^5))/(2-x^2)$ , or $(x^(5/2)(1+x^4))/(2-x^2)$

How do you simplify x^(3/2)((x+x^5)/(2-x^2))x^(3/2)((x+x^5)/(2-x^2))?