Tìm x:
a,\(\frac{x+1}{24}\)+\(\frac{x+2}{23}\)+\(\frac{x+3}{22}\)+\(\frac{x+4}{21}\)+4=0
b,\(\frac{x+2}{498}\)+\(\frac{x+3}{497}\)=\(\frac{x+4}{496}\)+\(\frac{x+5}{495}\)
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a) \(\frac{x+1}{24}+\frac{x+2}{23}+\frac{x+3}{22}+\frac{x+4}{21}+4=0\)
\(\Leftrightarrow\frac{x+1}{24}+1+\frac{x+2}{23}+1+\frac{x+3}{22}+1+\frac{x+4}{21}+1=0\)
\(\Leftrightarrow\frac{x+25}{24}+\frac{x+25}{23}+\frac{x+25}{22}+\frac{x+25}{21}=0\)
\(\Leftrightarrow\left(x+25\right)\left(\frac{1}{24}+\frac{1}{23}+\frac{1}{22}+\frac{1}{21}\right)=0\)
\(\Leftrightarrow x+25=0\)
\(\Leftrightarrow x=-25\)
b) \(\frac{x+2}{498}+\frac{x+3}{497}=\frac{x+4}{496}+\frac{x+5}{495}\)
\(\Leftrightarrow\frac{x+2}{498}+1+\frac{x+3}{497}+1=\frac{x+4}{496}+1+\frac{x+5}{495}+1\)
\(\Leftrightarrow\frac{x+500}{498}+\frac{x+500}{497}=\frac{x+500}{496}+\frac{x+500}{495}\)
\(\Leftrightarrow x+500=0\)
\(\Leftrightarrow x=-500\)