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

1 Answer
Jan 14, 2018

Answer:

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

Explanation:

#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)#