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\frac{5x^{2}+13x-26}{\left(x-1\right)\left(x^{2}-9\right)}
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\frac{5x^{2}+13x-26}{\left(x-1\right)\left(x^{2}-9\right)}
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\frac{5}{x-3}-\frac{x-2}{x^{2}-9}+\frac{1}{x-1}
Rewrite \left(x-1\right)^{2} as \left(x-1\right)\left(x-1\right). Cancel out x-1 in both numerator and denominator.
\frac{5}{x-3}-\frac{x-2}{\left(x-3\right)\left(x+3\right)}+\frac{1}{x-1}
Factor x^{2}-9.
\frac{5\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}-\frac{x-2}{\left(x-3\right)\left(x+3\right)}+\frac{1}{x-1}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-3 and \left(x-3\right)\left(x+3\right) is \left(x-3\right)\left(x+3\right). Multiply \frac{5}{x-3} times \frac{x+3}{x+3}.
\frac{5\left(x+3\right)-\left(x-2\right)}{\left(x-3\right)\left(x+3\right)}+\frac{1}{x-1}
Since \frac{5\left(x+3\right)}{\left(x-3\right)\left(x+3\right)} and \frac{x-2}{\left(x-3\right)\left(x+3\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{5x+15-x+2}{\left(x-3\right)\left(x+3\right)}+\frac{1}{x-1}
Do the multiplications in 5\left(x+3\right)-\left(x-2\right).
\frac{4x+17}{\left(x-3\right)\left(x+3\right)}+\frac{1}{x-1}
Combine like terms in 5x+15-x+2.
\frac{\left(4x+17\right)\left(x-1\right)}{\left(x-3\right)\left(x-1\right)\left(x+3\right)}+\frac{\left(x-3\right)\left(x+3\right)}{\left(x-3\right)\left(x-1\right)\left(x+3\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-3\right)\left(x+3\right) and x-1 is \left(x-3\right)\left(x-1\right)\left(x+3\right). Multiply \frac{4x+17}{\left(x-3\right)\left(x+3\right)} times \frac{x-1}{x-1}. Multiply \frac{1}{x-1} times \frac{\left(x-3\right)\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}.
\frac{\left(4x+17\right)\left(x-1\right)+\left(x-3\right)\left(x+3\right)}{\left(x-3\right)\left(x-1\right)\left(x+3\right)}
Since \frac{\left(4x+17\right)\left(x-1\right)}{\left(x-3\right)\left(x-1\right)\left(x+3\right)} and \frac{\left(x-3\right)\left(x+3\right)}{\left(x-3\right)\left(x-1\right)\left(x+3\right)} have the same denominator, add them by adding their numerators.
\frac{4x^{2}-4x+17x-17+x^{2}+3x-3x-9}{\left(x-3\right)\left(x-1\right)\left(x+3\right)}
Do the multiplications in \left(4x+17\right)\left(x-1\right)+\left(x-3\right)\left(x+3\right).
\frac{5x^{2}+13x-26}{\left(x-3\right)\left(x-1\right)\left(x+3\right)}
Combine like terms in 4x^{2}-4x+17x-17+x^{2}+3x-3x-9.
\frac{5x^{2}+13x-26}{x^{3}-x^{2}-9x+9}
Expand \left(x-3\right)\left(x-1\right)\left(x+3\right).
\frac{5}{x-3}-\frac{x-2}{x^{2}-9}+\frac{1}{x-1}
Rewrite \left(x-1\right)^{2} as \left(x-1\right)\left(x-1\right). Cancel out x-1 in both numerator and denominator.
\frac{5}{x-3}-\frac{x-2}{\left(x-3\right)\left(x+3\right)}+\frac{1}{x-1}
Factor x^{2}-9.
\frac{5\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}-\frac{x-2}{\left(x-3\right)\left(x+3\right)}+\frac{1}{x-1}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-3 and \left(x-3\right)\left(x+3\right) is \left(x-3\right)\left(x+3\right). Multiply \frac{5}{x-3} times \frac{x+3}{x+3}.
\frac{5\left(x+3\right)-\left(x-2\right)}{\left(x-3\right)\left(x+3\right)}+\frac{1}{x-1}
Since \frac{5\left(x+3\right)}{\left(x-3\right)\left(x+3\right)} and \frac{x-2}{\left(x-3\right)\left(x+3\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{5x+15-x+2}{\left(x-3\right)\left(x+3\right)}+\frac{1}{x-1}
Do the multiplications in 5\left(x+3\right)-\left(x-2\right).
\frac{4x+17}{\left(x-3\right)\left(x+3\right)}+\frac{1}{x-1}
Combine like terms in 5x+15-x+2.
\frac{\left(4x+17\right)\left(x-1\right)}{\left(x-3\right)\left(x-1\right)\left(x+3\right)}+\frac{\left(x-3\right)\left(x+3\right)}{\left(x-3\right)\left(x-1\right)\left(x+3\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-3\right)\left(x+3\right) and x-1 is \left(x-3\right)\left(x-1\right)\left(x+3\right). Multiply \frac{4x+17}{\left(x-3\right)\left(x+3\right)} times \frac{x-1}{x-1}. Multiply \frac{1}{x-1} times \frac{\left(x-3\right)\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}.
\frac{\left(4x+17\right)\left(x-1\right)+\left(x-3\right)\left(x+3\right)}{\left(x-3\right)\left(x-1\right)\left(x+3\right)}
Since \frac{\left(4x+17\right)\left(x-1\right)}{\left(x-3\right)\left(x-1\right)\left(x+3\right)} and \frac{\left(x-3\right)\left(x+3\right)}{\left(x-3\right)\left(x-1\right)\left(x+3\right)} have the same denominator, add them by adding their numerators.
\frac{4x^{2}-4x+17x-17+x^{2}+3x-3x-9}{\left(x-3\right)\left(x-1\right)\left(x+3\right)}
Do the multiplications in \left(4x+17\right)\left(x-1\right)+\left(x-3\right)\left(x+3\right).
\frac{5x^{2}+13x-26}{\left(x-3\right)\left(x-1\right)\left(x+3\right)}
Combine like terms in 4x^{2}-4x+17x-17+x^{2}+3x-3x-9.
\frac{5x^{2}+13x-26}{x^{3}-x^{2}-9x+9}
Expand \left(x-3\right)\left(x-1\right)\left(x+3\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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