Answer:
[tex]\frac{\frac{4}{5}}{\frac{1}{3}+\frac{1}{5}-\frac{3}{5}}=-12[/tex]
Step-by-step explanation:
Considering the expression
[tex]\frac{\frac{4}{5}}{\frac{1}{3}+\frac{1}{5}-\frac{3}{5}}[/tex]
Solution Steps:
[tex]\frac{\frac{4}{5}}{\frac{1}{3}+\frac{1}{5}-\frac{3}{5}}[/tex]
as
[tex]\mathrm{Combine\:the\:fractions\:}\frac{1}{5}-\frac{3}{5}:\quad -\frac{2}{5}[/tex]
so
[tex]=\frac{\frac{4}{5}}{\frac{1}{3}-\frac{2}{5}}[/tex]
[tex]\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{\frac{b}{c}}{a}=\frac{b}{c\:\cdot \:a}[/tex]
[tex]=\frac{4}{5\left(\frac{1}{3}-\frac{2}{5}\right)}[/tex]
join [tex]\frac{1}{3}-\frac{2}{5}:\quad -\frac{1}{15}[/tex]
so
[tex]=\frac{4}{5\left(-\frac{1}{15}\right)}[/tex]
[tex]\mathrm{Remove\:parentheses}:\quad \left(-a\right)=-a[/tex]
[tex]=\frac{4}{-5\cdot \frac{1}{15}}[/tex]
[tex]\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{-b}=-\frac{a}{b}[/tex]
[tex]=-\frac{4}{5\cdot \frac{1}{15}}[/tex]
[tex]\mathrm{Multiply\:}5\cdot \frac{1}{15}\::\quad \frac{1}{3}[/tex]
so
[tex]=-\frac{4}{\frac{1}{3}}[/tex]
[tex]\mathrm{Simplify}\:\frac{4}{\frac{1}{3}}:\quad \frac{12}{1}[/tex]
so
[tex]=-\frac{12}{1}[/tex]
[tex]\mathrm{Apply\:rule}\:\frac{a}{1}=a[/tex]
[tex]=-12[/tex]
Therefore
[tex]\frac{\frac{4}{5}}{\frac{1}{3}+\frac{1}{5}-\frac{3}{5}}=-12[/tex]
