To evaluate the expression \( 7^{-1} + 4^{-1} \), we first need to calculate each term separately.
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Calculate \( 7^{-1} \): \[ 7^{-1} = \frac{1}{7} \]
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Calculate \( 4^{-1} \): \[ 4^{-1} = \frac{1}{4} \]
Now, we can add these two fractions together: \[ 7^{-1} + 4^{-1} = \frac{1}{7} + \frac{1}{4} \]
To add these fractions, we need a common denominator. The least common multiple of 7 and 4 is 28.
Now, we convert each fraction: \[ \frac{1}{7} = \frac{4}{28} \] \[ \frac{1}{4} = \frac{7}{28} \]
Now we can add them: \[ \frac{4}{28} + \frac{7}{28} = \frac{4 + 7}{28} = \frac{11}{28} \]
Thus, the final result is: \[ 7^{-1} + 4^{-1} = \frac{11}{28} \]