확장 ((x^3+1)^2)/(x^3)

해법

확장

\frac{( x ^{3} + 1 ) ^{2}}{x ^{3}}

x^{3} + 2 + \frac{1}{x ^{3}}

솔루션 단계

\frac{( x ^{3} + 1 ) ^{2}}{x ^{3}}

(x^{3} + 1)^{2} = x^{6} + 2 x^{3} + 1

= \frac{x ^{6} + 2 x ^{3} + 1}{x ^{3}}

분수 규칙 적용:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{x ^{6} + 2 x ^{3} + 1}{x ^{3}} = \frac{x ^{6}}{x ^{3}} + \frac{2 x ^{3}}{x ^{3}} + \frac{1}{x ^{3}}

= \frac{x ^{6}}{x ^{3}} + \frac{2 x ^{3}}{x ^{3}} + \frac{1}{x ^{3}}

\frac{x ^{6}}{x ^{3}}

취소하다 :

x^{3}

= x^{3} + \frac{2 x ^{3}}{x ^{3}} + \frac{1}{x ^{3}}

\frac{2 x ^{3}}{x ^{3}}

취소하다 :

2

= x^{3} + 2 + \frac{1}{x ^{3}}