Problem
ALG-B1-M06-P004 A homogeneous fraction
#4
★☆☆☆☆ Level 1 of 5
Let \(x,y\neq 0\) and \(\frac{x}{y}+\frac{y}{x}=3\). Find \(\frac{(x+y)^2}{xy}\).
Expand \((x+y)^2\) and divide by \(xy\).
\(\frac{(x+y)^2}{xy}=\frac{x^2+2xy+y^2}{xy}=\frac{x}{y}+2+\frac{y}{x}=3+2=5\).
A good short problem for recognizing homogeneity.