Answer:
- [tex]\frac{61}{11}[/tex]
Step-by-step explanation:
[tex]\frac{x}{y}[/tex] = [tex]\frac{5}{6}[/tex] ( cross- multiply )
6x = 5y ( divide both sides by 6 )
x = [tex]\frac{5}{6}[/tex] y
Then
[tex]\frac{5x+6y}{5x-6y}[/tex] ← substitute x = [tex]\frac{5}{6}[/tex] y into the expression
= [tex]\frac{\frac{25}{6}y+6y }{\frac{25}{6}y-6y }[/tex]
= [tex]\frac{\frac{61}{6}y }{-\frac{11}{6}y }[/tex]
= [tex]\frac{\frac{61}{6} }{-\frac{11}{6} }[/tex]
= [tex]\frac{61}{6}[/tex] × - [tex]\frac{6}{11}[/tex]
= - [tex]\frac{61}{11}[/tex]
