Evaluate
\frac{7x^{2}+2x+10}{\left(x-2\right)\left(x+5\right)}
Expand
\frac{7x^{2}+2x+10}{\left(x-2\right)\left(x+5\right)}
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\frac{\left(2x+2\right)\left(x+5\right)}{\left(x-2\right)\left(x+5\right)}+\frac{5x\left(x-2\right)}{\left(x-2\right)\left(x+5\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-2 and x+5 is \left(x-2\right)\left(x+5\right). Multiply \frac{2x+2}{x-2} times \frac{x+5}{x+5}. Multiply \frac{5x}{x+5} times \frac{x-2}{x-2}.
\frac{\left(2x+2\right)\left(x+5\right)+5x\left(x-2\right)}{\left(x-2\right)\left(x+5\right)}
Since \frac{\left(2x+2\right)\left(x+5\right)}{\left(x-2\right)\left(x+5\right)} and \frac{5x\left(x-2\right)}{\left(x-2\right)\left(x+5\right)} have the same denominator, add them by adding their numerators.
\frac{2x^{2}+10x+2x+10+5x^{2}-10x}{\left(x-2\right)\left(x+5\right)}
Do the multiplications in \left(2x+2\right)\left(x+5\right)+5x\left(x-2\right).
\frac{7x^{2}+2x+10}{\left(x-2\right)\left(x+5\right)}
Combine like terms in 2x^{2}+10x+2x+10+5x^{2}-10x.
\frac{7x^{2}+2x+10}{x^{2}+3x-10}
Expand \left(x-2\right)\left(x+5\right).
\frac{\left(2x+2\right)\left(x+5\right)}{\left(x-2\right)\left(x+5\right)}+\frac{5x\left(x-2\right)}{\left(x-2\right)\left(x+5\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-2 and x+5 is \left(x-2\right)\left(x+5\right). Multiply \frac{2x+2}{x-2} times \frac{x+5}{x+5}. Multiply \frac{5x}{x+5} times \frac{x-2}{x-2}.
\frac{\left(2x+2\right)\left(x+5\right)+5x\left(x-2\right)}{\left(x-2\right)\left(x+5\right)}
Since \frac{\left(2x+2\right)\left(x+5\right)}{\left(x-2\right)\left(x+5\right)} and \frac{5x\left(x-2\right)}{\left(x-2\right)\left(x+5\right)} have the same denominator, add them by adding their numerators.
\frac{2x^{2}+10x+2x+10+5x^{2}-10x}{\left(x-2\right)\left(x+5\right)}
Do the multiplications in \left(2x+2\right)\left(x+5\right)+5x\left(x-2\right).
\frac{7x^{2}+2x+10}{\left(x-2\right)\left(x+5\right)}
Combine like terms in 2x^{2}+10x+2x+10+5x^{2}-10x.
\frac{7x^{2}+2x+10}{x^{2}+3x-10}
Expand \left(x-2\right)\left(x+5\right).
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Simultaneous equation
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Integration
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Limits
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