Evaluate
\frac{18y+17}{\left(y-1\right)\left(y+6\right)}
Expand
\frac{18y+17}{\left(y-1\right)\left(y+6\right)}
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\frac{\left(y+4\right)\left(y+6\right)}{\left(y-1\right)\left(y+6\right)}-\frac{\left(y-7\right)\left(y-1\right)}{\left(y-1\right)\left(y+6\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y-1 and y+6 is \left(y-1\right)\left(y+6\right). Multiply \frac{y+4}{y-1} times \frac{y+6}{y+6}. Multiply \frac{y-7}{y+6} times \frac{y-1}{y-1}.
\frac{\left(y+4\right)\left(y+6\right)-\left(y-7\right)\left(y-1\right)}{\left(y-1\right)\left(y+6\right)}
Since \frac{\left(y+4\right)\left(y+6\right)}{\left(y-1\right)\left(y+6\right)} and \frac{\left(y-7\right)\left(y-1\right)}{\left(y-1\right)\left(y+6\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{y^{2}+6y+4y+24-y^{2}+y+7y-7}{\left(y-1\right)\left(y+6\right)}
Do the multiplications in \left(y+4\right)\left(y+6\right)-\left(y-7\right)\left(y-1\right).
\frac{18y+17}{\left(y-1\right)\left(y+6\right)}
Combine like terms in y^{2}+6y+4y+24-y^{2}+y+7y-7.
\frac{18y+17}{y^{2}+5y-6}
Expand \left(y-1\right)\left(y+6\right).
\frac{\left(y+4\right)\left(y+6\right)}{\left(y-1\right)\left(y+6\right)}-\frac{\left(y-7\right)\left(y-1\right)}{\left(y-1\right)\left(y+6\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y-1 and y+6 is \left(y-1\right)\left(y+6\right). Multiply \frac{y+4}{y-1} times \frac{y+6}{y+6}. Multiply \frac{y-7}{y+6} times \frac{y-1}{y-1}.
\frac{\left(y+4\right)\left(y+6\right)-\left(y-7\right)\left(y-1\right)}{\left(y-1\right)\left(y+6\right)}
Since \frac{\left(y+4\right)\left(y+6\right)}{\left(y-1\right)\left(y+6\right)} and \frac{\left(y-7\right)\left(y-1\right)}{\left(y-1\right)\left(y+6\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{y^{2}+6y+4y+24-y^{2}+y+7y-7}{\left(y-1\right)\left(y+6\right)}
Do the multiplications in \left(y+4\right)\left(y+6\right)-\left(y-7\right)\left(y-1\right).
\frac{18y+17}{\left(y-1\right)\left(y+6\right)}
Combine like terms in y^{2}+6y+4y+24-y^{2}+y+7y-7.
\frac{18y+17}{y^{2}+5y-6}
Expand \left(y-1\right)\left(y+6\right).
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Simultaneous equation
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Differentiation
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Integration
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Limits
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