Solve (3^{-1}-4^-1)^-1+(2^-1+3^-1)

$$( 3 ^ { - 1 } - 4 ^ { - 1 } ) ^ { - 1 } + ( 2 ^ { - 1 } + 3 ^ { - 1 } )$$

Evaluate

$$\frac{77}{6}\approx 12.833333333$$

Solution Steps

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

$$\left(\frac{1}{3}-4^{-1}\right)^{-1}+2^{-1}+3^{-1}$$

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

$$\left(\frac{1}{3}-\frac{1}{4}\right)^{-1}+2^{-1}+3^{-1}$$

Subtract \frac{1}{4} from \frac{1}{3} to get \frac{1}{12}.

$$\left(\frac{1}{12}\right)^{-1}+2^{-1}+3^{-1}$$

Calculate \frac{1}{12} to the power of -1 and get 12.

$$12+2^{-1}+3^{-1}$$

Calculate 2 to the power of -1 and get \frac{1}{2}.

$$12+\frac{1}{2}+3^{-1}$$

Add 12 and \frac{1}{2} to get \frac{25}{2}.

$$\frac{25}{2}+3^{-1}$$

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

$$\frac{25}{2}+\frac{1}{3}$$

Add \frac{25}{2} and \frac{1}{3} to get \frac{77}{6}.

$$\frac{77}{6}$$

Factor

$$\frac{7 \cdot 11}{2 \cdot 3} = 12\frac{5}{6} = 12.833333333333334$$