Question

如果x/y=3,求x^2+xy+2y^2/x^2-xy+y^2

Answer 1

x/y=3
x=3y
所以xy=3y²
x²=9y²
所以原式=(9y²+3y²+2y²)/(9y²-3y²+y²)
=14y²/7y²
=2

Answer 2

x/y=3，则：
(x²＋xy＋2y²)/(x²－xy＋y²) 【分子分母同除以y²】
=[(x/y)²＋(x/y)＋2]/[(x/y)²－(x/y)＋1]
=[3²＋3＋2]/[3²－3＋1]
=14/7
=2