Question

已知x=2009,y=2010,求：

x²+2xy+y²/5x²-4xy ÷ x+y/5x-4y + x²-y/x 的值

Answer 1

原式=[(x²+2xy+y²)/(5x²-4xy)]÷[(x+y)/(5x-4y)]+[(x²-y)/x]
={ (x+y)²/[x(5x-4y)] }×[(5x-4y)/(x+y)]+[(x²-y)/x]
=[(x+y)/x]+[(x²-y)/x]
=(x+y+x²-y)/x
=(x²+x)/x
=x(x+1)/x
=x+1
=2009+1
=2010

Answer 2

x²+2xy+y²/5x²-4xy ÷ x+y/5x-4y + x²-y/x

=(x+y)^2/x*(5x-4y)*(5x-4y)/(x+y)+(x^2-y)/x
=(x+y)/x+(x^2-y)/x
=(x+y+x^2-y)/x
=(x+x^2)/x
=1+x
=1+2009
=2010