Evaluate
-\frac{3x^{2}+8x+3}{1-x^{2}}
Expand
-\frac{3x^{2}+8x+3}{1-x^{2}}
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\frac{1}{x-1}+\frac{2x+1}{\left(x-1\right)\left(x+1\right)}-\frac{3x^{2}+5x+1}{1-x^{2}}
Factor x^{2}-1.
\frac{x+1}{\left(x-1\right)\left(x+1\right)}+\frac{2x+1}{\left(x-1\right)\left(x+1\right)}-\frac{3x^{2}+5x+1}{1-x^{2}}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-1 and \left(x-1\right)\left(x+1\right) is \left(x-1\right)\left(x+1\right). Multiply \frac{1}{x-1} times \frac{x+1}{x+1}.
\frac{x+1+2x+1}{\left(x-1\right)\left(x+1\right)}-\frac{3x^{2}+5x+1}{1-x^{2}}
Since \frac{x+1}{\left(x-1\right)\left(x+1\right)} and \frac{2x+1}{\left(x-1\right)\left(x+1\right)} have the same denominator, add them by adding their numerators.
\frac{3x+2}{\left(x-1\right)\left(x+1\right)}-\frac{3x^{2}+5x+1}{1-x^{2}}
Combine like terms in x+1+2x+1.
\frac{3x+2}{\left(x-1\right)\left(x+1\right)}-\frac{3x^{2}+5x+1}{\left(x-1\right)\left(-x-1\right)}
Factor 1-x^{2}.
\frac{3x+2}{\left(x-1\right)\left(x+1\right)}-\frac{-\left(3x^{2}+5x+1\right)}{\left(x-1\right)\left(x+1\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-1\right)\left(x+1\right) and \left(x-1\right)\left(-x-1\right) is \left(x-1\right)\left(x+1\right). Multiply \frac{3x^{2}+5x+1}{\left(x-1\right)\left(-x-1\right)} times \frac{-1}{-1}.
\frac{3x+2-\left(-\left(3x^{2}+5x+1\right)\right)}{\left(x-1\right)\left(x+1\right)}
Since \frac{3x+2}{\left(x-1\right)\left(x+1\right)} and \frac{-\left(3x^{2}+5x+1\right)}{\left(x-1\right)\left(x+1\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{3x+2+3x^{2}+5x+1}{\left(x-1\right)\left(x+1\right)}
Do the multiplications in 3x+2-\left(-\left(3x^{2}+5x+1\right)\right).
\frac{8x+3+3x^{2}}{\left(x-1\right)\left(x+1\right)}
Combine like terms in 3x+2+3x^{2}+5x+1.
\frac{8x+3+3x^{2}}{x^{2}-1}
Expand \left(x-1\right)\left(x+1\right).
\frac{1}{x-1}+\frac{2x+1}{\left(x-1\right)\left(x+1\right)}-\frac{3x^{2}+5x+1}{1-x^{2}}
Factor x^{2}-1.
\frac{x+1}{\left(x-1\right)\left(x+1\right)}+\frac{2x+1}{\left(x-1\right)\left(x+1\right)}-\frac{3x^{2}+5x+1}{1-x^{2}}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-1 and \left(x-1\right)\left(x+1\right) is \left(x-1\right)\left(x+1\right). Multiply \frac{1}{x-1} times \frac{x+1}{x+1}.
\frac{x+1+2x+1}{\left(x-1\right)\left(x+1\right)}-\frac{3x^{2}+5x+1}{1-x^{2}}
Since \frac{x+1}{\left(x-1\right)\left(x+1\right)} and \frac{2x+1}{\left(x-1\right)\left(x+1\right)} have the same denominator, add them by adding their numerators.
\frac{3x+2}{\left(x-1\right)\left(x+1\right)}-\frac{3x^{2}+5x+1}{1-x^{2}}
Combine like terms in x+1+2x+1.
\frac{3x+2}{\left(x-1\right)\left(x+1\right)}-\frac{3x^{2}+5x+1}{\left(x-1\right)\left(-x-1\right)}
Factor 1-x^{2}.
\frac{3x+2}{\left(x-1\right)\left(x+1\right)}-\frac{-\left(3x^{2}+5x+1\right)}{\left(x-1\right)\left(x+1\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-1\right)\left(x+1\right) and \left(x-1\right)\left(-x-1\right) is \left(x-1\right)\left(x+1\right). Multiply \frac{3x^{2}+5x+1}{\left(x-1\right)\left(-x-1\right)} times \frac{-1}{-1}.
\frac{3x+2-\left(-\left(3x^{2}+5x+1\right)\right)}{\left(x-1\right)\left(x+1\right)}
Since \frac{3x+2}{\left(x-1\right)\left(x+1\right)} and \frac{-\left(3x^{2}+5x+1\right)}{\left(x-1\right)\left(x+1\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{3x+2+3x^{2}+5x+1}{\left(x-1\right)\left(x+1\right)}
Do the multiplications in 3x+2-\left(-\left(3x^{2}+5x+1\right)\right).
\frac{8x+3+3x^{2}}{\left(x-1\right)\left(x+1\right)}
Combine like terms in 3x+2+3x^{2}+5x+1.
\frac{8x+3+3x^{2}}{x^{2}-1}
Expand \left(x-1\right)\left(x+1\right).
Examples
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y = 3x + 4
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Matrix
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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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