Question

Stuck on a math: Fraction exponent factoring and simplifying.

Answer 1

`(x+2)^{-(1)/(5)}-(x+2)^{-(6)/(5)}`

`\frac{1}{(x+2)^{(1)/(5)}}-\frac{1}{(x+2)^{(6)/(5)}}`

`\frac{1}{\sqrt[5]{x+2}}-\frac{1}{(x+2)\sqrt[5]{x+2}}`

`\boxed{\frac{x+1}{\sqrt[5]{x+2}\cdot(x+2)}}`

Hope this helps.

r3t40

Answer 2

Explanation:

(x+2)^(-1/5) - (x+2)^(-6/5)

Factor out (x+2)^(-1/5):

(x+2)^(-1/5) [ 1 - (x+2)^(-5/5) ]

(x+2)^(-1/5) [ 1 - (x+2)^-1 ]

(x+2)^(-1/5) [ 1 - 1/(x+2) ]

Common denominator:

(x+2)^(-1/5) [ (x+2)/(x+2) - 1/(x+2) ]

(x+2)^(-1/5) [ (x+2-1)/(x+2) ]

(x+2)^(-1/5) [ (x+1)/(x+2) ]