How do you combine #x^ { 3/ 2} ( \sqrt { x } - \frac { 1} { \sqrt { x } } )#?

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Answer 1 · 2018-05-12T02:51:53

#color(red)(x^(3/2) * (sqrtx - 1/sqrtx) = color(indigo)(=x^2 - x = x * (x - 1)#

Laws of Indices

#a^m * a^n = a^(m + n)#

#a^m / a^n = a^(m-n)#

#"Given "color(red)( x^(3/2) * (sqrtx - 1/sqrtx)#

#=> x^(3/2) * (x^(1/2) - 1/x^(1/2))#

#=> x^(3/2) * x^(1/2) - x^(3/2) / x^(1/2), " removing bracket"#

#=> x^((3/2) + (1/2)) - x^((3/2) - (1/2)), " applying laws of indices"#

#color(indigo)(=> x^2 - x = x * (x - 1)#