展開する ((r+θ)(r-θ))/(θ^2)

解

展開する

\frac{( r + θ ) ( r - θ )}{θ ^{2}}

\frac{r ^{2}}{θ ^{2}} - 1

解答ステップ

\frac{( r + θ ) ( r - θ )}{θ ^{2}}

拡張

(r + θ) (r - θ) : r^{2} - θ^{2}

= \frac{r ^{2} - θ ^{2}}{θ ^{2}}

分数の規則を適用する:

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

\frac{r ^{2} - θ ^{2}}{θ ^{2}} = \frac{r ^{2}}{θ ^{2}} - \frac{θ ^{2}}{θ ^{2}}

= \frac{r ^{2}}{θ ^{2}} - \frac{θ ^{2}}{θ ^{2}}

規則を適用

\frac{a}{a} = 1

\frac{θ ^{2}}{θ ^{2}} = 1

= \frac{r ^{2}}{θ ^{2}} - 1