[tex]\bf \cfrac{2}{z-5}=\cfrac{z}{0.5z^2+7}\implies \cfrac{2}{z-5}=\cfrac{z}{\frac{1}{2}z^2+7}\impliedby cross-multiplying
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2\left( \frac{1}{2}z^2+7 \right)=(z-5)z\implies z^2+14=z^2-5z
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\underline{z^2-z^2}+14=-5z\implies 14=-5z\implies \cfrac{14}{-5}=z[/tex]
