Question

4/5 divided by 1/3 plus 1/5 minus 3/5

Answer 1

`((4)/(5))/((1)/(3)+(1)/(5)-(3)/(5))=-12`

Explanation:

Considering the expression

`((4)/(5))/((1)/(3)+(1)/(5)-(3)/(5))`

Solution Steps:

`((4)/(5))/((1)/(3)+(1)/(5)-(3)/(5))`

as

`\mathrm{Combine\:the\:fractions\:}(1)/(5)-(3)/(5):\quad -(2)/(5)`

so

`=((4)/(5))/((1)/(3)-(2)/(5))`

`\mathrm{Apply\:the\:fraction\:rule}:\quad ((b)/(c))/(a)=(b)/(c\:\cdot \:a)`

`=(4)/(5\left((1)/(3)-(2)/(5)\right))`

join
`(1)/(3)-(2)/(5):\quad -(1)/(15)`

so

`=(4)/(5\left(-(1)/(15)\right))`

`\mathrm{Remove\:parentheses}:\quad \left(-a\right)=-a`

`=(4)/(-5\cdot (1)/(15))`

`\mathrm{Apply\:the\:fraction\:rule}:\quad (a)/(-b)=-(a)/(b)`

`=-(4)/(5\cdot (1)/(15))`

`\mathrm{Multiply\:}5\cdot (1)/(15)\::\quad (1)/(3)`

so

`=-(4)/((1)/(3))`

`\mathrm{Simplify}\:(4)/((1)/(3)):\quad (12)/(1)`

so

`=-(12)/(1)`

`\mathrm{Apply\:rule}\:(a)/(1)=a`

`=-12`

Therefore

`((4)/(5))/((1)/(3)+(1)/(5)-(3)/(5))=-12`