What is expand 1/(sqrt(1-\frac{v^2){c^2)}} ?

The solution to expand 1/(sqrt(1-\frac{v^2){c^2)}} is (csqrt(c^2-v^2))/(c^2-v^2)

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expand 1/(sqrt(1-\frac{v^2){c^2)}}

expand

\frac{1}{1 - \frac{v ^{2}}{c ^{2}}}

\frac{c c ^{2} - v ^{2}}{c ^{2} - v ^{2}}

Solution steps

\frac{1}{1 - \frac{v ^{2}}{c ^{2}}}

1 - \frac{v ^{2}}{c ^{2}} = \frac{c ^{2} - v ^{2}}{c}

= \frac{1}{\frac{c ^{2} - v ^{2}}{c}}

Apply the fraction rule:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

= \frac{c}{c ^{2} - v ^{2}}

Rationalize

\frac{c}{c ^{2} - v ^{2}} : \frac{c - v ^{2} + c ^{2}}{- v ^{2} + c ^{2}}

= \frac{c - v ^{2} + c ^{2}}{c ^{2} - v ^{2}}

\frac{1}{x ( 1 + t x )}

x y d x - (2 x + 4 y) d y

\frac{2 x}{( z + x ) ( z - x )}

\frac{1}{( ( s + 17.824 ) ( s + 14.645 ) )}

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

What is expand 1/(sqrt(1-\frac{v^2){c^2)}} ?
The solution to expand 1/(sqrt(1-\frac{v^2){c^2)}} is (csqrt(c^2-v^2))/(c^2-v^2)