What is expand ((r+θ)(r-θ))/(θ^2) ?

The solution to expand ((r+θ)(r-θ))/(θ^2) is (r^2)/(θ^2)-1

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expand ((r+θ)(r-θ))/(θ^2)

expand

\frac{( r + θ ) ( r - θ )}{θ ^{2}}

\frac{r ^{2}}{θ ^{2}} - 1

Solution steps

\frac{( r + θ ) ( r - θ )}{θ ^{2}}

Expand

(r + θ) (r - θ) : r^{2} - θ^{2}

= \frac{r ^{2} - θ ^{2}}{θ ^{2}}

Apply the fraction rule:

\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}}

Apply rule

\frac{a}{a} = 1

\frac{θ ^{2}}{θ ^{2}} = 1

= \frac{r ^{2}}{θ ^{2}} - 1

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What is expand ((r+θ)(r-θ))/(θ^2) ?
The solution to expand ((r+θ)(r-θ))/(θ^2) is (r^2)/(θ^2)-1