Answer:
Step-by-step explanation:
Alright, lets get started.
Suppose the first fraction is : ![\frac{a}{b}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%7D%7Bb%7D)
Suppose the second fraction is : ![\frac{c}{d}](https://tex.z-dn.net/?f=%5Cfrac%7Bc%7D%7Bd%7D)
The sum of both fraction is given as : ![\frac{5}{6}](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B6%7D)
.......................equation (1)
The difference of both fraction is given as : ![\frac{1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D)
.........................equation (2)
Adding equation (1) and equation (2)
![\frac{c}{d} \ will \ be \ cancelled](https://tex.z-dn.net/?f=%5Cfrac%7Bc%7D%7Bd%7D%20%5C%20will%20%20%5C%20be%20%5C%20cancelled)
![\frac{2a}{b}=\frac{5}{6}+\frac{1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B2a%7D%7Bb%7D%3D%5Cfrac%7B5%7D%7B6%7D%2B%5Cfrac%7B1%7D%7B2%7D)
making common denominator
![\frac{2a}{b}=\frac{5}{6}+ \frac{3}{6}](https://tex.z-dn.net/?f=%5Cfrac%7B2a%7D%7Bb%7D%3D%5Cfrac%7B5%7D%7B6%7D%2B%20%5Cfrac%7B3%7D%7B6%7D)
![\frac{2a}{b}=\frac{8}{6}](https://tex.z-dn.net/?f=%5Cfrac%7B2a%7D%7Bb%7D%3D%5Cfrac%7B8%7D%7B6%7D)
Hence,
![\frac{a}{b}=\frac{2}{3}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%7D%7Bb%7D%3D%5Cfrac%7B2%7D%7B3%7D)
Plugging the value of
in equation (1)
![\frac{2}{3}+\frac{c}{d}=\frac{5}{6}](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B3%7D%2B%5Cfrac%7Bc%7D%7Bd%7D%3D%5Cfrac%7B5%7D%7B6%7D)
Subtracting
in both sides
![\frac{c}{d}=\frac{5}{6}-\frac{2}{3}](https://tex.z-dn.net/?f=%5Cfrac%7Bc%7D%7Bd%7D%3D%5Cfrac%7B5%7D%7B6%7D-%5Cfrac%7B2%7D%7B3%7D)
![\frac{c}{d}=\frac{1}{6}](https://tex.z-dn.net/?f=%5Cfrac%7Bc%7D%7Bd%7D%3D%5Cfrac%7B1%7D%7B6%7D)
Hence both fractions are
...................Answer
Hope it will help :)