\(\left(x-3\right)\left(x+5\right)=0\)

\(\Rightarrow\orbr{\begin{cases}x-3=0\\x+5=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=3\\x=-5\end{cases}}\)

(x-3)x(x+5)=0

\(\Rightarrow\orbr{\begin{cases}x-3=0\\x+5=0\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=0+3\\x=0-5\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=3\\x=-5\end{cases}}\)

Vậy \(\orbr{\begin{cases}x=3\\x=-5\end{cases}}\)

a)1/1x2+1/2x3+....+1/2003x2004

=1-1/2+1/2-1/3+...+1/2003+1/2004

=1-1/2004

=2004/2004-1/2004

=2003/2004

b)1/1x3+1/3x5+...+1/2003x2005

=1-1/3+1/3-1/5+....+1/2003+1/2005

=1-1/2005

=2005/2005-1/2005

=2004/2005

2004/2005

a) \(\frac{4}{20}+\frac{16}{42}+\frac{6}{15}+\frac{-3}{5}+\frac{2}{21}+\frac{-10}{21}+\frac{3}{20}\)

\(=\frac{1}{5}+\frac{8}{21}+\frac{2}{5}+\frac{-3}{5}+\frac{2}{21}+\frac{-10}{21}+\frac{3}{20}\)

= \(\left(\frac{1}{5}+\frac{2}{5}+\frac{-3}{5}\right)+\left(\frac{8}{21}+\frac{2}{21}+\frac{-10}{21}\right)+\frac{3}{20}\)

\(=\frac{0}{5}+\frac{0}{21}+\frac{3}{20}\)

\(=0+0+\frac{3}{20}\)

\(=\frac{3}{20}\)

 b) \(\frac{42}{46}+\frac{250}{186}+\frac{-2121}{2323}+\frac{-125125}{143143}\)

\(=\frac{21}{23}+\frac{125}{93}+\frac{-21}{23}+\frac{-125}{143}\)

\(=\left(\frac{21}{23}+\frac{-21}{23}\right)+\frac{125}{93}+\frac{-125}{143}\)

\(=0+\frac{125}{93}+\frac{-125}{143}\)

\(=\frac{17875}{13299}+\frac{-11625}{13299}\)

\(=\frac{6250}{13299}\)

(Hình như câu b hơi sai)

\(a)\frac{4}{20}+\frac{16}{42}+\frac{6}{15}+\frac{-3}{5}+\frac{2}{21}+\frac{10}{21}+\frac{3}{20}\)

\(=\frac{1}{5}+\frac{8}{21}+\frac{2}{5}+\frac{-3}{5}+\frac{2}{21}+\frac{-10}{21}+\frac{3}{20}\)

\(=\left(\frac{1}{5}+\frac{2}{5}+\frac{-3}{5}\right)+\left(\frac{8}{21}+\frac{2}{21}+\frac{-10}{21}\right)+\frac{3}{20}\)

\(=0+0+\frac{3}{20}\)

\(=\frac{3}{20}\)

\(\frac{3}{x+5}=15\%\)

\(\Rightarrow3:\left(x+5\right)=15\%\)

\(x+5=3:15\%\)

\(x+5=20\)

\(x=20-5\)

\(x=15\)

\(\frac{3}{x+5}=15\%\)

\(\frac{3}{x+5}=\frac{3}{20}\)

\(\Rightarrow x+5=20\)

\(\Rightarrow x=15\)

234 - 345 = -111

234 - 345 = -111

\(a.\frac{2\cdot\left(-13\right)\cdot9\cdot10}{\left(-3\right)\cdot4\cdot\left(-5\right)\cdot26}\)

\(=\frac{2\cdot\left(-13\right)\cdot3\cdot3\cdot2\cdot5}{\left(-3\right)\cdot2\cdot2\cdot\left(-5\right)\cdot13\cdot2}\)

\(=-\frac{3}{2}\)

b) \(\frac{2^3\cdot3^4}{2^2\cdot3^2\cdot5}=\frac{2\cdot3^2}{5}=\frac{2\cdot9}{5}=\frac{18}{5}\)

\(\frac{2^4\cdot5^2\cdot11^2\cdot7}{2^3\cdot5^3\cdot7^2\cdot11}=\frac{2\cdot1\cdot11\cdot1}{1\cdot5\cdot7\cdot1}=\frac{22}{35}\)

c) \(\frac{121\cdot75\cdot130\cdot169}{39\cdot60\cdot11\cdot198}=\frac{11\cdot11\cdot13\cdot10\cdot169}{13\cdot3\cdot6\cdot10\cdot11\cdot11\cdot6\cdot3}\)

\(=\frac{169}{3\cdot6\cdot6\cdot3}=\frac{169}{324}\)

d) \(\frac{1998\cdot1990+3978}{1992\cdot1991-3984}\)