Question

3. Efectuați calculele și prezentați rezultatul sub forma unei fracții ireductibile.
Va rog dau coroana ​

Answer 1

Răspuns:

Explicație pas cu pas:

g)

x/(2x+1) + 1/(2x+1) + (3x+1)/(2x+1)  = 2

= (x + 1 + 3 x + 1 ) / ( 2 x + 1 ) =

= ( 4 x + 2 ) / ( 2 x + 1 ) =

= 2(2 x + 1 ) / ( 2 x + 1 ) =  => simplific cu ( 2 x + 1)

= 2

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h)

( 3 a + 2 b ) / ( a + b ) + ( 2 a + 3 b ) / ( a + b ) = 5

= ( 3 a + 2 b + 2 a + 3 b ) / ( a + b ) =

= ( 5 a + 5 b ) / ( a + b ) =

= 5(a+b) / (a+b) =

= 5

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i)

___             ___           __

abc/999  + cab/999 + bca/999 =(a+b+c)/9

= (100a+10b+c+100c+10a+b+100b+10c+a)/999 =

= (111a+111b+111c)/999 =

= 111(a+b+c)/999 = => simplific cu 111

= (a+b+c)/9

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j)

(5a+3)/(3a+6) - 3 a/(3a+6) + 1/(3a+6) = 2/3

= ( 5 a + 3 - 3 a + 1 ) /(3a+6) =

=(2a+4)/(3a+6) =

= 2(a+2)/3(a+2)=

= 2/3

______________________________

k)

2014/2014 - 2013/2014 + 2012/2014 - 2011/2014+ ...... + 2/2014 - 1/2014 =1/2

= ( 2014-2013+2012-2011+.....+2-1)/2014 =

= [( 2014-2013) + (2012-2011) + ( 2010-2009) +....+ ( 2-1) ]/2014=

=>   2014 : 2 = 1007 diferente sau: ( 2013 - 1) : 2 + 1 = 1007 nr. impare

= (1+1+1+.....+1)/2014 =

= 1 × 1007/2014 =

= 1/2

Answer 2

Explicație pas cu pas:

g.

$\frac{x + 1 + 3x + 1}{2x + 1} = \frac{4x + 2}{2x + 1} = \\ \frac{2(2x + 1)}{2 x + 1} = \frac{2}{1} = 2$

h.

$\frac{3x + 2y + 2x + 3y}{x + y} = \frac{5x + 5y}{x + y} = \\ \frac{5(x + y)}{x + y} = \frac{5}{1} = 5$

i.

$\frac{111a + 111b + 111c}{999} = \frac{111(a + b + c)}{999} = \frac{a + b + c}{9}$

j. ???

K.

$\frac{2014}{2014} - \frac{2013}{2014} + \frac{2012}{2014} - \frac{2011}{2014} + ... \\ + \frac{2}{2014} - \frac{1}{2014} = \frac{1 \times (2014 \div 2)}{2014} \\ = \frac{1007}{2014} = \frac{1}{2}$