Evaluate
\frac{x^{2}+x+4}{x^{2}-1}
Expand
\frac{x^{2}+x+4}{x^{2}-1}
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\frac{\left(x-1\right)\left(x+2\right)}{\left(x+1\right)\left(x+2\right)}+\frac{3x+3}{x^{2}-1}
Factor the expressions that are not already factored in \frac{x^{2}+x-2}{x^{2}+3x+2}.
\frac{x-1}{x+1}+\frac{3x+3}{x^{2}-1}
Cancel out x+2 in both numerator and denominator.
\frac{x-1}{x+1}+\frac{3\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}
Factor the expressions that are not already factored in \frac{3x+3}{x^{2}-1}.
\frac{x-1}{x+1}+\frac{3}{x-1}
Cancel out x+1 in both numerator and denominator.
\frac{\left(x-1\right)\left(x-1\right)}{\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 x+1 and x-1 is \left(x-1\right)\left(x+1\right). Multiply \frac{x-1}{x+1} times \frac{x-1}{x-1}. Multiply \frac{3}{x-1} times \frac{x+1}{x+1}.
\frac{\left(x-1\right)\left(x-1\right)+3\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}
Since \frac{\left(x-1\right)\left(x-1\right)}{\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^{2}-x-x+1+3x+3}{\left(x-1\right)\left(x+1\right)}
Do the multiplications in \left(x-1\right)\left(x-1\right)+3\left(x+1\right).
\frac{x^{2}+x+4}{\left(x-1\right)\left(x+1\right)}
Combine like terms in x^{2}-x-x+1+3x+3.
\frac{x^{2}+x+4}{x^{2}-1}
Expand \left(x-1\right)\left(x+1\right).
\frac{\left(x-1\right)\left(x+2\right)}{\left(x+1\right)\left(x+2\right)}+\frac{3x+3}{x^{2}-1}
Factor the expressions that are not already factored in \frac{x^{2}+x-2}{x^{2}+3x+2}.
\frac{x-1}{x+1}+\frac{3x+3}{x^{2}-1}
Cancel out x+2 in both numerator and denominator.
\frac{x-1}{x+1}+\frac{3\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}
Factor the expressions that are not already factored in \frac{3x+3}{x^{2}-1}.
\frac{x-1}{x+1}+\frac{3}{x-1}
Cancel out x+1 in both numerator and denominator.
\frac{\left(x-1\right)\left(x-1\right)}{\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 x+1 and x-1 is \left(x-1\right)\left(x+1\right). Multiply \frac{x-1}{x+1} times \frac{x-1}{x-1}. Multiply \frac{3}{x-1} times \frac{x+1}{x+1}.
\frac{\left(x-1\right)\left(x-1\right)+3\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}
Since \frac{\left(x-1\right)\left(x-1\right)}{\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^{2}-x-x+1+3x+3}{\left(x-1\right)\left(x+1\right)}
Do the multiplications in \left(x-1\right)\left(x-1\right)+3\left(x+1\right).
\frac{x^{2}+x+4}{\left(x-1\right)\left(x+1\right)}
Combine like terms in x^{2}-x-x+1+3x+3.
\frac{x^{2}+x+4}{x^{2}-1}
Expand \left(x-1\right)\left(x+1\right).
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\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
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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