Question

(x^2+y^2)/(x+y) is homogeneous with degree.

Answer 1

Let E = ( x² + y² ) / ( x + y )

To find the degree of this homogeneous expression put y = ty, x = tx

[ (tx) ² + ( ty) ²] / [ tx + ty ]

[ t²x² + t²y² ] / t ( x + y )

t² ( x² + y² ) / t ( x + y )

t [ ( x² + y² ) / ( x + y ) ]

t × E

Since power of t is one hence degree of this homogeneous expression is 1

Answer 2

Answer:

$\frac{(x^2+y^2)}{(x+y)}=\frac{(x+y)^2-2xy}{x+y} =x+y-\frac{2xy}{x+y}$

Degree of first two terms is 1 and the third term is 2.

∴ They are not homogenous by degree.