Phân tích mẫu của $VT.$$\mathfrak{Bài toán 3:}$ Giãi phương trình:
$ a,$ $ \dfrac{\begin{pmatrix}\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4} + ... + \dfrac{1}{2005}\end{pmatrix}x}{2004+\dfrac{2003}{2}+\dfrac{2002}{3}+...+ \dfrac{1}{2004}}=2005$
Ta có:
$2004+\frac{2003}{2}+\frac{2002}{3}+...+\frac{1}{2004}$
$=\frac{2005-1}{1}+\frac{2005-2}{2}+\frac{2005-3}{3}+...+\frac{2005-(2005-1)}{2005-1}$
$=2005-1+\frac{2005}{2}-1+\frac{2005}{3}-1+...+\frac{2005}{2005-1}-1$
$=2005+\frac{2005}{2}+\frac{2005}{3}+...+\frac{2005}{2004}-2004$
$=1+2005\left ( \frac{1}{2}+\frac{1}{3}+...+\frac{1}{2004} \right )$
$=2005\left ( \frac{1}{2}+\frac{1}{3}+...+\frac{1}{2004}+\frac{1}{2005} \right )$
Tới đây dễ rồi ^^~.