Evaluate
\frac{2x+11}{\left(2-x\right)\left(2x-3\right)\left(x+1\right)}
Expand
\frac{2x+11}{\left(2-x\right)\left(2x-3\right)\left(x+1\right)}
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\frac{3\left(-x+2\right)}{\left(2x-3\right)\left(x+1\right)\left(-x+2\right)}+\frac{5\left(x+1\right)}{\left(2x-3\right)\left(x+1\right)\left(-x+2\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x+1\right)\left(2x-3\right) and \left(2x-3\right)\left(2-x\right) is \left(2x-3\right)\left(x+1\right)\left(-x+2\right). Multiply \frac{3}{\left(x+1\right)\left(2x-3\right)} times \frac{-x+2}{-x+2}. Multiply \frac{5}{\left(2x-3\right)\left(2-x\right)} times \frac{x+1}{x+1}.
\frac{3\left(-x+2\right)+5\left(x+1\right)}{\left(2x-3\right)\left(x+1\right)\left(-x+2\right)}
Since \frac{3\left(-x+2\right)}{\left(2x-3\right)\left(x+1\right)\left(-x+2\right)} and \frac{5\left(x+1\right)}{\left(2x-3\right)\left(x+1\right)\left(-x+2\right)} have the same denominator, add them by adding their numerators.
\frac{-3x+6+5x+5}{\left(2x-3\right)\left(x+1\right)\left(-x+2\right)}
Do the multiplications in 3\left(-x+2\right)+5\left(x+1\right).
\frac{2x+11}{\left(2x-3\right)\left(x+1\right)\left(-x+2\right)}
Combine like terms in -3x+6+5x+5.
\frac{2x+11}{-2x^{3}+5x^{2}+x-6}
Expand \left(2x-3\right)\left(x+1\right)\left(-x+2\right).
\frac{3\left(-x+2\right)}{\left(2x-3\right)\left(x+1\right)\left(-x+2\right)}+\frac{5\left(x+1\right)}{\left(2x-3\right)\left(x+1\right)\left(-x+2\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x+1\right)\left(2x-3\right) and \left(2x-3\right)\left(2-x\right) is \left(2x-3\right)\left(x+1\right)\left(-x+2\right). Multiply \frac{3}{\left(x+1\right)\left(2x-3\right)} times \frac{-x+2}{-x+2}. Multiply \frac{5}{\left(2x-3\right)\left(2-x\right)} times \frac{x+1}{x+1}.
\frac{3\left(-x+2\right)+5\left(x+1\right)}{\left(2x-3\right)\left(x+1\right)\left(-x+2\right)}
Since \frac{3\left(-x+2\right)}{\left(2x-3\right)\left(x+1\right)\left(-x+2\right)} and \frac{5\left(x+1\right)}{\left(2x-3\right)\left(x+1\right)\left(-x+2\right)} have the same denominator, add them by adding their numerators.
\frac{-3x+6+5x+5}{\left(2x-3\right)\left(x+1\right)\left(-x+2\right)}
Do the multiplications in 3\left(-x+2\right)+5\left(x+1\right).
\frac{2x+11}{\left(2x-3\right)\left(x+1\right)\left(-x+2\right)}
Combine like terms in -3x+6+5x+5.
\frac{2x+11}{-2x^{3}+5x^{2}+x-6}
Expand \left(2x-3\right)\left(x+1\right)\left(-x+2\right).
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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4 \sin \theta \cos \theta = 2 \sin \theta
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y = 3x + 4
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Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}