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\frac{\left(x+3\right)\left(x-2\right)}{\left(x-2\right)\left(x-1\right)}-\frac{\left(x+7\right)\left(x-1\right)}{\left(x-2\right)\left(x-1\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-1 and x-2 is \left(x-2\right)\left(x-1\right). Multiply \frac{x+3}{x-1} times \frac{x-2}{x-2}. Multiply \frac{x+7}{x-2} times \frac{x-1}{x-1}.
\frac{\left(x+3\right)\left(x-2\right)-\left(x+7\right)\left(x-1\right)}{\left(x-2\right)\left(x-1\right)}
Since \frac{\left(x+3\right)\left(x-2\right)}{\left(x-2\right)\left(x-1\right)} and \frac{\left(x+7\right)\left(x-1\right)}{\left(x-2\right)\left(x-1\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{x^{2}-2x+3x-6-x^{2}+x-7x+7}{\left(x-2\right)\left(x-1\right)}
Do the multiplications in \left(x+3\right)\left(x-2\right)-\left(x+7\right)\left(x-1\right).
\frac{-5x+1}{\left(x-2\right)\left(x-1\right)}
Combine like terms in x^{2}-2x+3x-6-x^{2}+x-7x+7.
\frac{-5x+1}{x^{2}-3x+2}
Expand \left(x-2\right)\left(x-1\right).
\frac{\left(x+3\right)\left(x-2\right)}{\left(x-2\right)\left(x-1\right)}-\frac{\left(x+7\right)\left(x-1\right)}{\left(x-2\right)\left(x-1\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-1 and x-2 is \left(x-2\right)\left(x-1\right). Multiply \frac{x+3}{x-1} times \frac{x-2}{x-2}. Multiply \frac{x+7}{x-2} times \frac{x-1}{x-1}.
\frac{\left(x+3\right)\left(x-2\right)-\left(x+7\right)\left(x-1\right)}{\left(x-2\right)\left(x-1\right)}
Since \frac{\left(x+3\right)\left(x-2\right)}{\left(x-2\right)\left(x-1\right)} and \frac{\left(x+7\right)\left(x-1\right)}{\left(x-2\right)\left(x-1\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{x^{2}-2x+3x-6-x^{2}+x-7x+7}{\left(x-2\right)\left(x-1\right)}
Do the multiplications in \left(x+3\right)\left(x-2\right)-\left(x+7\right)\left(x-1\right).
\frac{-5x+1}{\left(x-2\right)\left(x-1\right)}
Combine like terms in x^{2}-2x+3x-6-x^{2}+x-7x+7.
\frac{-5x+1}{x^{2}-3x+2}
Expand \left(x-2\right)\left(x-1\right).