Evaluate
\frac{4x}{x^{2}-1}
Expand
\frac{4x}{x^{2}-1}
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\frac{x-3}{\left(x-1\right)\left(x+1\right)}+\frac{3}{x-1}
Factor x^{2}-1.
\frac{x-3}{\left(x-1\right)\left(x+1\right)}+\frac{3\left(x+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 x-1 is \left(x-1\right)\left(x+1\right). Multiply \frac{3}{x-1} times \frac{x+1}{x+1}.
\frac{x-3+3\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}
Since \frac{x-3}{\left(x-1\right)\left(x+1\right)} and \frac{3\left(x+1\right)}{\left(x-1\right)\left(x+1\right)} have the same denominator, add them by adding their numerators.
\frac{x-3+3x+3}{\left(x-1\right)\left(x+1\right)}
Do the multiplications in x-3+3\left(x+1\right).
\frac{4x}{\left(x-1\right)\left(x+1\right)}
Combine like terms in x-3+3x+3.
\frac{4x}{x^{2}-1}
Expand \left(x-1\right)\left(x+1\right).
\frac{x-3}{\left(x-1\right)\left(x+1\right)}+\frac{3}{x-1}
Factor x^{2}-1.
\frac{x-3}{\left(x-1\right)\left(x+1\right)}+\frac{3\left(x+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 x-1 is \left(x-1\right)\left(x+1\right). Multiply \frac{3}{x-1} times \frac{x+1}{x+1}.
\frac{x-3+3\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}
Since \frac{x-3}{\left(x-1\right)\left(x+1\right)} and \frac{3\left(x+1\right)}{\left(x-1\right)\left(x+1\right)} have the same denominator, add them by adding their numerators.
\frac{x-3+3x+3}{\left(x-1\right)\left(x+1\right)}
Do the multiplications in x-3+3\left(x+1\right).
\frac{4x}{\left(x-1\right)\left(x+1\right)}
Combine like terms in x-3+3x+3.
\frac{4x}{x^{2}-1}
Expand \left(x-1\right)\left(x+1\right).
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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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