Question

if : \(\large{\frac{1}{x+1}+\frac{2}{y+2}+\frac{2006}{z+2006}=1}\)
find the value of :
\(\large{\frac{x^2}{x^2+x}+\frac{y^2}{y^2+2y}+\frac{z^2}{z^2+2006z}}\)

Answer 1

@ash2326 , @ajprincess @mathavraj

Answer 2

I did like this :
\[\large{(\frac{x}{x+1})+(\frac{y}{y+2})+(\frac{z}{z+2006})}\]

Answer 3

but what to do next?:

Answer 4

Do long division for each fraction.

Answer 5

\[x/(x+1) = 1-(1/x+1)\]

Answer 6

\[2/(y+2) = 1-2/(y+2)\]

Answer 7

does it make sense ??