Solve =[3^-1+4^-1+5^-1]^-1

$$= [ 3 ^ { - 1 } + 4 ^ { - 1 } + 5 ^ { - 1 } ] ^ { - 1 }$$

Evaluate

$$\frac{60}{47}\approx 1.276595745$$

Solution Steps

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

$$\left(\frac{1}{3}+4^{-1}+5^{-1}\right)^{-1}$$

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

$$\left(\frac{1}{3}+\frac{1}{4}+5^{-1}\right)^{-1}$$

Add \frac{1}{3} and \frac{1}{4} to get \frac{7}{12}.

$$\left(\frac{7}{12}+5^{-1}\right)^{-1}$$

Calculate 5 to the power of -1 and get \frac{1}{5}.

$$\left(\frac{7}{12}+\frac{1}{5}\right)^{-1}$$

Add \frac{7}{12} and \frac{1}{5} to get \frac{47}{60}.

$$\left(\frac{47}{60}\right)^{-1}$$

Calculate \frac{47}{60} to the power of -1 and get \frac{60}{47}.

$$\frac{60}{47}$$

Factor

$$\frac{2 ^ {2} \cdot 3 \cdot 5}{47} = 1\frac{13}{47} = 1.2765957446808511$$