Evaluate
z+1-\frac{6}{z}
Expand
z+1-\frac{6}{z}
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\frac{\left(z^{2}-4\right)\left(z+3\right)}{z\left(z+2\right)}
Divide \frac{z^{2}-4}{z} by \frac{z+2}{z+3} by multiplying \frac{z^{2}-4}{z} by the reciprocal of \frac{z+2}{z+3}.
\frac{\left(z-2\right)\left(z+2\right)\left(z+3\right)}{z\left(z+2\right)}
Factor the expressions that are not already factored.
\frac{\left(z-2\right)\left(z+3\right)}{z}
Cancel out z+2 in both numerator and denominator.
\frac{z^{2}+z-6}{z}
Expand the expression.
\frac{\left(z^{2}-4\right)\left(z+3\right)}{z\left(z+2\right)}
Divide \frac{z^{2}-4}{z} by \frac{z+2}{z+3} by multiplying \frac{z^{2}-4}{z} by the reciprocal of \frac{z+2}{z+3}.
\frac{\left(z-2\right)\left(z+2\right)\left(z+3\right)}{z\left(z+2\right)}
Factor the expressions that are not already factored.
\frac{\left(z-2\right)\left(z+3\right)}{z}
Cancel out z+2 in both numerator and denominator.
\frac{z^{2}+z-6}{z}
Expand the expression.
Examples
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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
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}