What is (1/C+1/(3*(1/C+1/C)^{-1)})^{-1} ?

The solution to (1/C+1/(3*(1/C+1/C)^{-1)})^{-1} is (3C)/5

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simplify (1/C+1/(3*(1/C+1/C)^{-1)})^{-1}

simplify

(\frac{1}{C} + \frac{1}{3 \cdot ( \frac{1}{C} + \frac{1}{C} ) ^{- 1}})^{- 1}

\frac{3 C}{5}

Solution steps

(\frac{1}{C} + \frac{1}{3 ( \frac{1}{C} + \frac{1}{C} ) ^{- 1}})^{- 1}

Apply exponent rule:

a^{- 1} = \frac{1}{a}

(\frac{1}{C} + \frac{1}{3 ( \frac{1}{C} + \frac{1}{C} ) ^{- 1}})^{- 1} = \frac{1}{\frac{1}{C} + \frac{1}{3 ( \frac{1}{C} + \frac{1}{C} ) ^{- 1}}}

= \frac{1}{\frac{1}{C} + \frac{1}{3 ( \frac{1}{C} + \frac{1}{C} ) ^{- 1}}}

Combine the fractions

\frac{1}{C} + \frac{1}{C} : \frac{2}{C}

= \frac{1}{\frac{1}{C} + \frac{1}{3 ( \frac{2}{C} ) ^{- 1}}}

\frac{1}{3 ( \frac{2}{C} ) ^{- 1}} = \frac{2}{3 C}

= \frac{1}{\frac{1}{C} + \frac{2}{3 C}}

Join

\frac{1}{C} + \frac{2}{3 C} : \frac{5}{3 C}

= \frac{1}{\frac{5}{3 C}}

Apply the fraction rule:

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

= \frac{3 C}{5}

3 x + 8 = 2 x + 24

\frac{5}{3} = \frac{t}{6}

t - 12 = - 4

x^{2} - 2 x + 50 = 0

\frac{x}{5} + 3 = 9

What is (1/C+1/(3*(1/C+1/C)^{-1)})^{-1} ?
The solution to (1/C+1/(3*(1/C+1/C)^{-1)})^{-1} is (3C)/5