Bài 1: 1.1.Tìm x a, 3/35-(3/5+x)=2/7 b, 5x(2x-1/3)=0 c, 6(x-1)+2x(x-1)=0 1.2.Tính nhanh a, A=8/9-1/72-1/56-1/42-1/30-1/20-1/12-1/6-1/2 b, B=0,75-0,6+

Đáp án:

 $1.1
a) x=\dfrac{-4}{5}\\
b) {\left[\begin{aligned}x=0\\x=\dfrac{1}{6}\end{aligned}\right.}\\
c)  {\left[\begin{aligned}x=1\\x=-3\end{aligned}\right.}\\
1.2)
a)
A=0\\
b)
B=\dfrac{3}{11}$

Giải thích các bước giải:

 $1.1
a) \dfrac{3}{35}-\left ( \dfrac{3}{5}+x \right )=\dfrac{2}{7}\\
\Leftrightarrow \dfrac{3}{35}-\dfrac{3}{5}-x=\dfrac{2}{7}\\
\Leftrightarrow x=\dfrac{3}{35}-\dfrac{3}{5}-\dfrac{2}{7}\\
\Leftrightarrow x=\dfrac{3}{35}-\dfrac{21}{35}-\dfrac{10}{35}\\
\Leftrightarrow x=\dfrac{-28}{35}=\dfrac{-4}{5}$
$b) 5x.\left ( 2x-\dfrac{1}{3} \right) =0\\
\Leftrightarrow {\left[\begin{aligned}5x=0\\2x-\dfrac{1}{3}=0\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned}x=0\\2x=\dfrac{1}{3}\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned}x=0\\x=\dfrac{1}{6}\end{aligned}\right.}$
$c) 6(x-1)+2x(x-1)=0\\
\Leftrightarrow 2(x-1)(3+x)=0\\
\Leftrightarrow {\left[\begin{aligned}x-1=0\\x+3=0\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned}x=1\\x=-3\end{aligned}\right.}$
$1.2)
a)
A=\dfrac{8}{9}-\dfrac{1}{72}-\dfrac{1}{56}-\dfrac{1}{42}-\dfrac{1}{30}-\dfrac{1}{20}-\dfrac{1}{12}-\dfrac{1}{6}-\dfrac{1}{2}\\
=-\left ( \dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}+\dfrac{1}{72} \right )+\dfrac{8}{9}\\
=-\left ( \dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}+\dfrac{1}{6.7}+\dfrac{1}{7.8}+\dfrac{1}{8.9} \right )+\dfrac{8}{9}\\
=-\left ( 1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{9} \right )+\dfrac{8}{9}\\
=-\left ( 1-\dfrac{1}{9} \right )+\dfrac{8}{9}\\
=-1+\dfrac{1}{9}+\dfrac{8}{9}\\
=-1+1\\
=0$
$b)
B=\dfrac{0,75-0,6+\dfrac{3}{7}+\dfrac{3}{13}}{2,75-2,2+\dfrac{11}{7}+\dfrac{11}{13}}\\
=\dfrac{\dfrac{3}{4}-\dfrac{3}{5}+\dfrac{3}{7}+\dfrac{3}{13}}{\dfrac{11}{4}-\dfrac{11}{5}+\dfrac{11}{7}+\dfrac{11}{13}}\\
=\dfrac{3.\left (\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{7}+\dfrac{1}{13}  \right )}{11.\left (\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{7}+\dfrac{1}{13}  \right )}\\
=\dfrac{3}{11}$