Answer:
[tex]=-12[/tex]
Step-by-step explanation:
[tex]\frac{7\frac{1}{2}}{4\frac{1}{2}-5\frac{1}{8}}\\\mathrm{Convert\:mixed\:numbers\:to\:improper\:fractions}:\quad 7\frac{1}{2}=\frac{15}{2}\\\frac{\frac{15}{2}}{4\frac{1}{2}-5\frac{1}{8}}\\\mathrm{Convert\:mixed\:numbers\:to\:improper\:fractions}:\quad 4\frac{1}{2}=\frac{9}{2}\\\frac{\frac{15}{2}}{\frac{9}{2}-5\frac{1}{8}}\\\mathrm{Convert\:mixed\:numbers\:to\:improper\:fractions}:\quad 5\frac{1}{8}=\frac{41}{8}\\\frac{\frac{15}{2}}{\frac{9}{2}-\frac{41}{8}}[/tex]
[tex]\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{\frac{b}{c}}{a}=\frac{b}{c\:\cdot \:a}\\=\frac{15}{2\left(\frac{9}{2}-\frac{41}{8}\right)}\\\mathrm{Join}\:\frac{9}{2}-\frac{41}{8}:\quad -\frac{5}{8}\\=\frac{15}{2\left(-\frac{5}{8}\right)}\\\mathrm{Remove\:parentheses}:\quad \left(-a\right)=-a\\=\frac{15}{-2\cdot \frac{5}{8}}\\\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{-b}=-\frac{a}{b}\\=-\frac{15}{2\cdot \frac{5}{8}}\\\mathrm{Multiply\:}2\cdot \frac{5}{8}\::\quad \frac{5}{4}[/tex]
[tex]=-\frac{15}{\frac{5}{4}}\\\mathrm{Simplify}\:\frac{15}{\frac{5}{4}}:\quad \frac{60}{5}\\\mathrm{Divide\:the\:numbers:}\:\frac{60}{5}=12\\=-12[/tex]
