Evaluate
\frac{z-3}{z}
Expand
\frac{z-3}{z}
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\frac{\left(z^{2}+6z+8\right)\left(z^{2}+2z-15\right)}{\left(z^{2}+9z+20\right)\left(z^{2}+2z\right)}
Divide \frac{z^{2}+6z+8}{z^{2}+9z+20} by \frac{z^{2}+2z}{z^{2}+2z-15} by multiplying \frac{z^{2}+6z+8}{z^{2}+9z+20} by the reciprocal of \frac{z^{2}+2z}{z^{2}+2z-15}.
\frac{\left(z-3\right)\left(z+2\right)\left(z+4\right)\left(z+5\right)}{z\left(z+2\right)\left(z+4\right)\left(z+5\right)}
Factor the expressions that are not already factored.
\frac{z-3}{z}
Cancel out \left(z+2\right)\left(z+4\right)\left(z+5\right) in both numerator and denominator.
\frac{\left(z^{2}+6z+8\right)\left(z^{2}+2z-15\right)}{\left(z^{2}+9z+20\right)\left(z^{2}+2z\right)}
Divide \frac{z^{2}+6z+8}{z^{2}+9z+20} by \frac{z^{2}+2z}{z^{2}+2z-15} by multiplying \frac{z^{2}+6z+8}{z^{2}+9z+20} by the reciprocal of \frac{z^{2}+2z}{z^{2}+2z-15}.
\frac{\left(z-3\right)\left(z+2\right)\left(z+4\right)\left(z+5\right)}{z\left(z+2\right)\left(z+4\right)\left(z+5\right)}
Factor the expressions that are not already factored.
\frac{z-3}{z}
Cancel out \left(z+2\right)\left(z+4\right)\left(z+5\right) in both numerator and denominator.
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Limits
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