Evaluate
\frac{20x^{4}+10x^{3}-13x-14}{\left(x+3\right)\left(2x+1\right)}
Expand
\frac{20x^{4}+10x^{3}-13x-14}{\left(x+3\right)\left(2x+1\right)}
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\frac{\left(10x^{3}-5\right)\left(2x+1\right)}{\left(x+3\right)\left(2x+1\right)}-\frac{3\left(x+3\right)}{\left(x+3\right)\left(2x+1\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x+3 and 2x+1 is \left(x+3\right)\left(2x+1\right). Multiply \frac{10x^{3}-5}{x+3} times \frac{2x+1}{2x+1}. Multiply \frac{3}{2x+1} times \frac{x+3}{x+3}.
\frac{\left(10x^{3}-5\right)\left(2x+1\right)-3\left(x+3\right)}{\left(x+3\right)\left(2x+1\right)}
Since \frac{\left(10x^{3}-5\right)\left(2x+1\right)}{\left(x+3\right)\left(2x+1\right)} and \frac{3\left(x+3\right)}{\left(x+3\right)\left(2x+1\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{20x^{4}+10x^{3}-10x-5-3x-9}{\left(x+3\right)\left(2x+1\right)}
Do the multiplications in \left(10x^{3}-5\right)\left(2x+1\right)-3\left(x+3\right).
\frac{20x^{4}+10x^{3}-13x-14}{\left(x+3\right)\left(2x+1\right)}
Combine like terms in 20x^{4}+10x^{3}-10x-5-3x-9.
\frac{20x^{4}+10x^{3}-13x-14}{2x^{2}+7x+3}
Expand \left(x+3\right)\left(2x+1\right).
\frac{\left(10x^{3}-5\right)\left(2x+1\right)}{\left(x+3\right)\left(2x+1\right)}-\frac{3\left(x+3\right)}{\left(x+3\right)\left(2x+1\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x+3 and 2x+1 is \left(x+3\right)\left(2x+1\right). Multiply \frac{10x^{3}-5}{x+3} times \frac{2x+1}{2x+1}. Multiply \frac{3}{2x+1} times \frac{x+3}{x+3}.
\frac{\left(10x^{3}-5\right)\left(2x+1\right)-3\left(x+3\right)}{\left(x+3\right)\left(2x+1\right)}
Since \frac{\left(10x^{3}-5\right)\left(2x+1\right)}{\left(x+3\right)\left(2x+1\right)} and \frac{3\left(x+3\right)}{\left(x+3\right)\left(2x+1\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{20x^{4}+10x^{3}-10x-5-3x-9}{\left(x+3\right)\left(2x+1\right)}
Do the multiplications in \left(10x^{3}-5\right)\left(2x+1\right)-3\left(x+3\right).
\frac{20x^{4}+10x^{3}-13x-14}{\left(x+3\right)\left(2x+1\right)}
Combine like terms in 20x^{4}+10x^{3}-10x-5-3x-9.
\frac{20x^{4}+10x^{3}-13x-14}{2x^{2}+7x+3}
Expand \left(x+3\right)\left(2x+1\right).
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Simultaneous equation
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Integration
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Limits
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