Question

已知（x+2y）/x=4，求（x^2+y^2)/(x^2-xy-y^2)的值

Answer 1

（x+2y）/x= 1+2y/x =4
故 y/x = 3/2
（x^2+y^2)/(x^2-xy-y^2)
=[1+(y/x)^2]/[1-y/x -(y/x)]^2
=(1+9/4)(1-3/2-9/4)
=13/4 /(-11/4)
=-13/11

Answer 2

（x+2y）/x=4，
x+2y=4x
y=3x/2
把y=3x/2代人（x^2+y^2)/(x^2-xy-y^2)得：
[x²+(3x/2)²]/[x²-x(3x/2)-(3x/2)²]
=(x²+9/4x²)/(x²-3x²/2-9x²/4)
=13x²/4/[(4x²-6x²-9x²)/4]
=13x²/4/(-11x²/4)
=-13/11