Reviewing for precalc and I dont understand how to completely factor expressions with rational exponents. a) x^frac{5}{2} - 9x^{frac{1}{2}} b) x^{-frac{2}{3}}+2x(-frac{1}{2})+x^{frac{1}{2}}

Josalynn 2021-02-19 Answered
Reviewing for precalc and I dont understand how to completely factor expressions with rational exponents.
a)x529x12
b)x23+2x(12)+x12
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Expert Answer

Layton
Answered 2021-02-20 Author has 89 answers

a)Given:
x529x12
On simplification, we get
x529x12=x2x129x12[xmxn=xm+nx2x12=x2+12=x52]
=x12(x29)
=x12(x232)
=x12(x3)(x+3)[a2b2)=(ab)(a+b)]
b)Given:
=x32+2x(12)+x12
On simplification, we get
x32+2x(12)+x12=x32+2x(32)x+x32x2[(xmxn=xm+n(x32x=x32+1=x12)
And x32x2=x32+2=x12
x32(1+2x+x2)
=x32(1+x)2[(1+x)2=1+2x+x2]

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