Evaluate
\frac{4x^{3}-4x^{2}+2x-1}{\left(2x-3\right)\left(x+1\right)}
Expand
\frac{4x^{3}-4x^{2}+2x-1}{2x^{2}-x-3}
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2x-1+\frac{7x-4}{\left(2x-3\right)\left(x+1\right)}
Factor 2x^{2}-x-3.
\frac{\left(2x-1\right)\left(2x-3\right)\left(x+1\right)}{\left(2x-3\right)\left(x+1\right)}+\frac{7x-4}{\left(2x-3\right)\left(x+1\right)}
To add or subtract expressions, expand them to make their denominators the same. Multiply 2x-1 times \frac{\left(2x-3\right)\left(x+1\right)}{\left(2x-3\right)\left(x+1\right)}.
\frac{\left(2x-1\right)\left(2x-3\right)\left(x+1\right)+7x-4}{\left(2x-3\right)\left(x+1\right)}
Since \frac{\left(2x-1\right)\left(2x-3\right)\left(x+1\right)}{\left(2x-3\right)\left(x+1\right)} and \frac{7x-4}{\left(2x-3\right)\left(x+1\right)} have the same denominator, add them by adding their numerators.
\frac{4x^{3}-2x^{2}-6x-2x^{2}+x+3+7x-4}{\left(2x-3\right)\left(x+1\right)}
Do the multiplications in \left(2x-1\right)\left(2x-3\right)\left(x+1\right)+7x-4.
\frac{4x^{3}-4x^{2}+2x-1}{\left(2x-3\right)\left(x+1\right)}
Combine like terms in 4x^{3}-2x^{2}-6x-2x^{2}+x+3+7x-4.
\frac{4x^{3}-4x^{2}+2x-1}{2x^{2}-x-3}
Expand \left(2x-3\right)\left(x+1\right).
2x-1+\frac{7x-4}{\left(2x-3\right)\left(x+1\right)}
Factor 2x^{2}-x-3.
\frac{\left(2x-1\right)\left(2x-3\right)\left(x+1\right)}{\left(2x-3\right)\left(x+1\right)}+\frac{7x-4}{\left(2x-3\right)\left(x+1\right)}
To add or subtract expressions, expand them to make their denominators the same. Multiply 2x-1 times \frac{\left(2x-3\right)\left(x+1\right)}{\left(2x-3\right)\left(x+1\right)}.
\frac{\left(2x-1\right)\left(2x-3\right)\left(x+1\right)+7x-4}{\left(2x-3\right)\left(x+1\right)}
Since \frac{\left(2x-1\right)\left(2x-3\right)\left(x+1\right)}{\left(2x-3\right)\left(x+1\right)} and \frac{7x-4}{\left(2x-3\right)\left(x+1\right)} have the same denominator, add them by adding their numerators.
\frac{4x^{3}-2x^{2}-6x-2x^{2}+x+3+7x-4}{\left(2x-3\right)\left(x+1\right)}
Do the multiplications in \left(2x-1\right)\left(2x-3\right)\left(x+1\right)+7x-4.
\frac{4x^{3}-4x^{2}+2x-1}{\left(2x-3\right)\left(x+1\right)}
Combine like terms in 4x^{3}-2x^{2}-6x-2x^{2}+x+3+7x-4.
\frac{4x^{3}-4x^{2}+2x-1}{2x^{2}-x-3}
Expand \left(2x-3\right)\left(x+1\right).
Examples
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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
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