(5/14 + 9/10) - 5/7

To solve the expression \((5/14 + 9/10) - 5/7\), we first need to find a common denominator for the fractions involved. The denominators are 14, 10, and 7.

The least common multiple (LCM) of 14, 10, and 7 is 70. Now we will convert each fraction to have a denominator of 70.

1. Convert \(5/14\): \[ \frac{5}{14} = \frac{5 \times 5}{14 \times 5} = \frac{25}{70} \]

2. Convert \(9/10\): \[ \frac{9}{10} = \frac{9 \times 7}{10 \times 7} = \frac{63}{70} \]

3. Convert \(5/7\): \[ \frac{5}{7} = \frac{5 \times 10}{7 \times 10} = \frac{50}{70} \]

Now substituting these back into the expression: \[ \left(\frac{25}{70} + \frac{63}{70}\right) - \frac{50}{70} \]

Now we can add the first two fractions: \[ \frac{25 + 63}{70} = \frac{88}{70} \]

Now we perform the subtraction: \[ \frac{88}{70} - \frac{50}{70} = \frac{88 - 50}{70} = \frac{38}{70} \]

Finally, we can simplify \(\frac{38}{70}\): \[ \frac{38}{70} = \frac{19}{35} \]

Thus, the result of the expression \((5/14 + 9/10) - 5/7\) is: \[ \frac{19}{35} \]