Solve 3/(3^-1+6^-1)div(frac{3{4})^-1}

$$\frac { 3 } { ( 3 ^ { - 1 } + 6 ^ { - 1 } ) \div ( \frac { 3 } { 4 } ) ^ { - 1 } }$$

Evaluate

$$8$$

Solution Steps

Divide 3 by \frac{3^{-1}+6^{-1}}{\left(\frac{3}{4}\right)^{-1}} by multiplying 3 by the reciprocal of \frac{3^{-1}+6^{-1}}{\left(\frac{3}{4}\right)^{-1}}.

$$\frac{3\times \left(\frac{3}{4}\right)^{-1}}{3^{-1}+6^{-1}}$$

Calculate \frac{3}{4} to the power of -1 and get \frac{4}{3}.

$$\frac{3\times \frac{4}{3}}{3^{-1}+6^{-1}}$$

Multiply 3 and \frac{4}{3} to get 4.

$$\frac{4}{3^{-1}+6^{-1}}$$

Calculate 3 to the power of -1 and get \frac{1}{3}.

$$\frac{4}{\frac{1}{3}+6^{-1}}$$

Calculate 6 to the power of -1 and get \frac{1}{6}.

$$\frac{4}{\frac{1}{3}+\frac{1}{6}}$$

Add \frac{1}{3} and \frac{1}{6} to get \frac{1}{2}.

$$\frac{4}{\frac{1}{2}}$$

Divide 4 by \frac{1}{2} by multiplying 4 by the reciprocal of \frac{1}{2}.

$$4\times 2$$

Multiply 4 and 2 to get 8.

$$8$$

Factor

$$2^{3}$$