Question

[Vũ Ngân Hà]

Tìm x(x>0)

\(\frac{2015}{2014}+\frac{1}{x}=\frac{1}{x+1}+\frac{2014}{2013}\)

Answer 1

[Nguyễn Phương Thuỳ]

Ta có 1+1/2014 +1/x=1/(x+1)+1+1/2013 nên 1/x-1/(x+1)=1/2013-1/(2013+1) nên x=2013

Answer 2

[Bùi Thế Hào]

Ta có: \(\frac{1}{x}-\frac{1}{x+1}=\frac{2014}{2013}-\frac{2015}{2014}\)

<=> \(\frac{1}{x\left(x+1\right)}=\frac{2014^2-2015.2013}{2013.2014}=\frac{1}{2013.2014}\)

<=> x(x+1)=2013.2014

=> x=2013

Đáp số: x=2013