Evaluate
\frac{5x^{2}-11x-9}{\left(x-3\right)\left(x+8\right)}
Expand
\frac{5x^{2}-11x-9}{\left(x-3\right)\left(x+8\right)}
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\frac{5x}{x+8}+\frac{4x-9}{\left(x-3\right)\left(x+8\right)}
Factor x^{2}+5x-24.
\frac{5x\left(x-3\right)}{\left(x-3\right)\left(x+8\right)}+\frac{4x-9}{\left(x-3\right)\left(x+8\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x+8 and \left(x-3\right)\left(x+8\right) is \left(x-3\right)\left(x+8\right). Multiply \frac{5x}{x+8} times \frac{x-3}{x-3}.
\frac{5x\left(x-3\right)+4x-9}{\left(x-3\right)\left(x+8\right)}
Since \frac{5x\left(x-3\right)}{\left(x-3\right)\left(x+8\right)} and \frac{4x-9}{\left(x-3\right)\left(x+8\right)} have the same denominator, add them by adding their numerators.
\frac{5x^{2}-15x+4x-9}{\left(x-3\right)\left(x+8\right)}
Do the multiplications in 5x\left(x-3\right)+4x-9.
\frac{5x^{2}-11x-9}{\left(x-3\right)\left(x+8\right)}
Combine like terms in 5x^{2}-15x+4x-9.
\frac{5x^{2}-11x-9}{x^{2}+5x-24}
Expand \left(x-3\right)\left(x+8\right).
\frac{5x}{x+8}+\frac{4x-9}{\left(x-3\right)\left(x+8\right)}
Factor x^{2}+5x-24.
\frac{5x\left(x-3\right)}{\left(x-3\right)\left(x+8\right)}+\frac{4x-9}{\left(x-3\right)\left(x+8\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x+8 and \left(x-3\right)\left(x+8\right) is \left(x-3\right)\left(x+8\right). Multiply \frac{5x}{x+8} times \frac{x-3}{x-3}.
\frac{5x\left(x-3\right)+4x-9}{\left(x-3\right)\left(x+8\right)}
Since \frac{5x\left(x-3\right)}{\left(x-3\right)\left(x+8\right)} and \frac{4x-9}{\left(x-3\right)\left(x+8\right)} have the same denominator, add them by adding their numerators.
\frac{5x^{2}-15x+4x-9}{\left(x-3\right)\left(x+8\right)}
Do the multiplications in 5x\left(x-3\right)+4x-9.
\frac{5x^{2}-11x-9}{\left(x-3\right)\left(x+8\right)}
Combine like terms in 5x^{2}-15x+4x-9.
\frac{5x^{2}-11x-9}{x^{2}+5x-24}
Expand \left(x-3\right)\left(x+8\right).
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\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
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