0,(1) = 1/9

0.(01) = 1/99

1,(8) = 17/9

0,27 = 3/11

\(\dfrac{37}{63}\) : 5 + \(\dfrac{37}{63}\) : 14 = \(\dfrac{37}{63}\) x ( 1/5 + 1/14) # \(\dfrac{37}{63}\) : (5 + 14)

\(\dfrac{25}{12}\).0,8  + \(\dfrac{25}{12}\) . 0,5  = \(\dfrac{25}{12}\). ( 0,8 + 0,5)

   0,8 : { 0,2 - 8 .[ \(\dfrac{7}{48}\)+ ( \(\dfrac{5}{24}\) - \(\dfrac{5}{26}\) ) ] }

= 0,8 : { 0,2 - 8.[ \(\dfrac{7}{48}\) -  \(\dfrac{5}{48}\)]}

= 0,8 : { 0,2 - 8. \(\dfrac{2}{48}\)}

= 0,8 : (0,2 - 1/3)

= 0,8 : (-2/15)

= - 0,8 . 15/2

= - 6 

   \([\)( \(\dfrac{3}{5}\) - \(\dfrac{1}{3}\)) .6 - \(\dfrac{1}{3}\)\(]\) .5

=\([\) \(\dfrac{4}{15}\) .6 - \(\dfrac{1}{3}\) \(]\) . 5 

= \([\) \(\dfrac{4}{5}\) .2 - \(\dfrac{1}{3}\) \(]\) . 5

= 8 - \(\dfrac{5}{3}\)

= 19/3

= 12

   ( 1 - \(\dfrac{2}{3}\) - \(\dfrac{1}{4}\) ) .( \(\dfrac{4}{5}\) - \(\dfrac{3}{4}\) )²

= ( \(\dfrac{1}{3}-\dfrac{1}{4}\)).\(\dfrac{1}{20^2}\)

= \(\dfrac{1}{12}\) . \(\dfrac{1}{400}\)

= \(\dfrac{1}{4800}\)

A = x² +10x + 1

A = (x² + 2.5x + 25) - 24

A = (x+5)² - 24

( x + 5)² ≥ 0 ⇔ (x + 5)² - 24 ≥ -24 

A (min) = - 24 ⇔ x = -5

\(\left(\dfrac{2}{5}x-2\right):\left(\dfrac{-3}{2}\right)=\dfrac{1}{3}\\ \Leftrightarrow\dfrac{2}{5}x-2=\dfrac{1}{3}.\dfrac{-3}{2}\\ \Leftrightarrow\dfrac{2}{5}x-2=\dfrac{-1}{2}\\ \Leftrightarrow\dfrac{2}{5}x=\dfrac{-1}{2}+2=\dfrac{-3}{2}\\ \Rightarrow x=\dfrac{-3}{2}:\dfrac{2}{5}=\dfrac{-3}{2}.\dfrac{2}{5}=\dfrac{-3}{5}\)

(\(\dfrac{2}{5}x\) - 2 ) : ( -\(\dfrac{3}{2}\) ) =  \(\dfrac{1}{3}\)

\(\dfrac{2}{5}x\)  -  2  =  \(\dfrac{1}{3}\).\((-\dfrac{3}{2})\)

\(\dfrac{2}{5}x\) - 2 =  \(-\dfrac{1}{2}\)

\(\dfrac{2}{5}\)\(x\)   =   2 - \(\dfrac{1}{2}\)

\(\dfrac{2}{5}x\) = \(\dfrac{3}{2}\)

\(x\) = \(\dfrac{3}{2}\) : \(\dfrac{2}{5}\)

\(x\) = \(\dfrac{15}{4}\)