ai giúp mik vsss:((

ƯC là viết tắt của "Ước chung"

dễ

Gọi \(ƯCLN\left(3n+2,6n+5\right)=d\)  \(\left(d\inℕ^∗\right)\)

\(\Rightarrow\left\{{}\begin{matrix}3n+2⋮d\\6n+5⋮d\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}6n+4⋮d\\6n+5⋮d\end{matrix}\right.\)

\(\Rightarrow\left(6n+5\right)-\left(6n+4\right)⋮d\)

\(\Rightarrow1⋮d\)

\(\Rightarrow d=1\)

Vậy \(ƯCLN\left(3n+2,6n+5\right)=1\) \(\Rightarrowđpcm\)

Gọi ƯCLN(3n +2; 6n + 5) =  d

Ta có:   \(\left\{{}\begin{matrix}3n+2⋮d\\6n+5⋮d\end{matrix}\right.\)

            \(\left\{{}\begin{matrix}2.\left(3n+2\right)⋮d\\6n+5⋮d\end{matrix}\right.\)

            \(\left\{{}\begin{matrix}6n+4⋮d\\6n+5⋮d\end{matrix}\right.\)

             6n + 5 - (6n+4) \(⋮\) d

            6n + 5 - 6n - 4 ⋮ d

                                 1 ⋮ d

               d = 1

Vậy \(\dfrac{3n+2}{6n+5}\) là phân số tối giản. (Đpcm)

Lời giải:
$2K=\frac{3-1}{1.2.3}+\frac{4-2}{2.3.4}+\frac{5-3}{3.4.5}+....+\frac{50-48}{48.49.50}$

$=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+....+\frac{1}{48.49}-\frac{1}{49.50}$

$=\frac{1}{1.2}-\frac{1}{49.50}=\frac{612}{1225}$

$\Rightarrow K=\frac{306}{1225}$

G = \(\dfrac{1}{1.2}\)+\(\dfrac{1}{2.3}\)+\(\dfrac{1}{3.4}\)+...+\(\dfrac{1}{49.50}\)

G = \(\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{49}-\dfrac{1}{50}\)

G = \(\dfrac{1}{1}\) - \(\dfrac{1}{50}\)

G = \(\dfrac{49}{50}\)

Lời giải:

a. $(a+b-c)-(-a-b+c)=a+b-c+a+b-c=(a+a)+(b+b)-(c+c)=2a+2b-2c$

b. $(a-b+c)-(a+b-c)=a-b+c-a-b+c=(a-a)-(b+b)+(c+c)=-2b+2c$

c. $-(x-y+z)+(x-y-z)=-x+y-z+x-y-z=(-x+x)+(y-y)-(z+z)=-2z$

d. $-(x-y+z)-(-x+y+z)=-x+y-z+x-y-z=(-x+x)+(y-y)-(z+z)=-2z$

a) ( a + b - c ) - ( - a -  b + c ) = a + b - c + a + b - c

b) ( a - b + c ) - ( a + b - c ) = a - b + c - a - b + c

c ) - ( x - y + z ) + ( x - y - z ) = -x + y - z + x - y - z

d) - ( x - y + z ) - ( - x + y + z ) = -x + y - z + x - y - z

Lời giải:
a) $(195-58)-(35-63)=195-58-35+63$

$=(195-35)+(63-58)$

$=160+5=165$

b) $-(77-162)+(47-59)=-77+162+47-59$

$=-(77-47)+(162-59)=-30+103=73$

c) $(-234-166)-(73-262)=-(234+166)+(262-73)$

$=-400+189=-(400-189)=-211$

d) $-(30-4)-(1975-2007)=-30+4-1975+2007=(2007+4)-(1975+30)$

$=2011-2005=6$

-17 - (-37) × 4 = 131

   -17 - (-37).4

= -17 + 37.4

= -17 + 148

= -17 + 148

= 131