Evaluate
\frac{x+57}{22\left(5x-1\right)}
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\frac{x+57}{22\left(5x-1\right)}
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\frac{22\left(3x+2\right)}{22\left(5x-1\right)}-\frac{13\left(5x-1\right)}{22\left(5x-1\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5x-1 and 22 is 22\left(5x-1\right). Multiply \frac{3x+2}{5x-1} times \frac{22}{22}. Multiply \frac{13}{22} times \frac{5x-1}{5x-1}.
\frac{22\left(3x+2\right)-13\left(5x-1\right)}{22\left(5x-1\right)}
Since \frac{22\left(3x+2\right)}{22\left(5x-1\right)} and \frac{13\left(5x-1\right)}{22\left(5x-1\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{66x+44-65x+13}{22\left(5x-1\right)}
Do the multiplications in 22\left(3x+2\right)-13\left(5x-1\right).
\frac{x+57}{22\left(5x-1\right)}
Combine like terms in 66x+44-65x+13.
\frac{x+57}{110x-22}
Expand 22\left(5x-1\right).
\frac{22\left(3x+2\right)}{22\left(5x-1\right)}-\frac{13\left(5x-1\right)}{22\left(5x-1\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5x-1 and 22 is 22\left(5x-1\right). Multiply \frac{3x+2}{5x-1} times \frac{22}{22}. Multiply \frac{13}{22} times \frac{5x-1}{5x-1}.
\frac{22\left(3x+2\right)-13\left(5x-1\right)}{22\left(5x-1\right)}
Since \frac{22\left(3x+2\right)}{22\left(5x-1\right)} and \frac{13\left(5x-1\right)}{22\left(5x-1\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{66x+44-65x+13}{22\left(5x-1\right)}
Do the multiplications in 22\left(3x+2\right)-13\left(5x-1\right).
\frac{x+57}{22\left(5x-1\right)}
Combine like terms in 66x+44-65x+13.
\frac{x+57}{110x-22}
Expand 22\left(5x-1\right).
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