Respuesta :
Answer:
Step-by-step explanation:
Alright, lets get started.
Suppose the first fraction is : [tex]\frac{a}{b}[/tex]
Suppose the second fraction is : [tex]\frac{c}{d}[/tex]
The sum of both fraction is given as : [tex]\frac{5}{6}[/tex]
[tex]\frac{a}{b}+\frac{c}{d}=\frac{5}{6}[/tex] .......................equation (1)
The difference of both fraction is given as : [tex]\frac{1}{2}[/tex]
[tex]\frac{a}{b}-\frac{c}{d}=\frac{1}{2}[/tex] .........................equation (2)
Adding equation (1) and equation (2)
[tex]\frac{c}{d} \ will \ be \ cancelled[/tex]
[tex]\frac{2a}{b}=\frac{5}{6}+\frac{1}{2}[/tex]
making common denominator
[tex]\frac{2a}{b}=\frac{5}{6}+ \frac{3}{6}[/tex]
[tex]\frac{2a}{b}=\frac{8}{6}[/tex]
Hence,
[tex]\frac{a}{b}=\frac{2}{3}[/tex]
Plugging the value of [tex]\frac{a}{b}[/tex] in equation (1)
[tex]\frac{2}{3}+\frac{c}{d}=\frac{5}{6}[/tex]
Subtracting [tex]\frac{2}{3}[/tex] in both sides
[tex]\frac{c}{d}=\frac{5}{6}-\frac{2}{3}[/tex]
[tex]\frac{c}{d}=\frac{1}{6}[/tex]
Hence both fractions are [tex]\frac{2}{3} \ and \ \frac{1}{6}[/tex] ...................Answer
Hope it will help :)
