a, 

\(=\frac{1}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{x.\left(x+2\right)}\right)\)

\(=\frac{1}{2}\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{x}-\frac{1}{x+2}\right)\)

\(=\frac{1}{2}\left(1-\frac{1}{x+2}\right)\)

\(=\frac{1}{2}\times\frac{x+1}{x+2}\)

\(=\frac{2x+2}{x+2}\)

Hơ hơ =v

Làm đại phần a đúng sai mặc kệ ~~

a,

\(\frac{1}{1\cdot3}+\frac{1}{3\cdot5}+\frac{1}{5\cdot7}+...+\frac{1}{x\left(x+2\right)}\)

\(=\frac{1}{2}\left(\frac{2}{1\cdot3}+\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+...+\frac{2}{x\left(x+2\right)}\right)\)

\(=\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{x}-\frac{1}{x+2}\right)\)

\(=\frac{1}{2}\left(1-\frac{1}{x+2}\right)\)

\(=\frac{1}{2}\cdot\frac{x+1}{x+2}\)

\(=\frac{2x+2}{x+2}\)

b,

x = 1.2 + 2.3 + 3.4 + ....+ 89.90

3x = 1.2.3 + 2.3.3 + 3.4.3 + .... + 89.90

3x = 1.2.3 + 2.3.(4 - 1) + 3.4.(5 - 2) + ... + 89.90.(91 - 88)

3x = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ... + 89.90.91 - 88.89.90

3x = 89.90.91

x = \(\frac{89\cdot90\cdot91}{3}=242970\)

a) Đặt \(A=\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{x.\left(x+2\right)}\)

\(\Rightarrow2A=(1-\frac{1}{3})+(\frac{1}{3}-\frac{1}{5})+...+(\frac{1}{x}-\frac{1}{x+2})\)

\(\Rightarrow A=1-\frac{1}{x+2}=\frac{x+1}{x+2}\)

b)\(x=1.2+2.3+3.4+...+89.90\)

\(\Rightarrow3x=1.2.(3-0)+2.3.(4-1)+...+89.98.(100-88)\)

\(\Rightarrow3x=1.2.3+2.3.4-1.2.3+...+89.90.100-88.89.90\)

\(\Rightarrow3x=89.90.100=872200\)

\(\Rightarrow x=\frac{872200}{3}\)

= 20 125 000 !!!

La 20125000

50x50x230x35=????

\(a,-2.\left(x+7\right)+3.\left(x-2\right)=-2\)

                \(-2x-14+3x-6=-2\)

                                         \(x-20=-2\)

                                                    \(x=-2+20\)

                                                    \(x=18\)

\(b,-7-2x=-37-\left(-26\right)\)

      \(-7-2x=-11\)

               \(-2x=-11+7\)

               \(-2x=-4\)

                     \(x=2\)

\(c,\left(3x+9\right).\left(11-x\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}3x+9=0\\11-x=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=-3\\x=11\end{cases}}}\)

\(\orbr{\begin{cases}3x+9=0\\11-x=0\end{cases}}\Rightarrow\orbr{\begin{cases}3x=-9\\x=11\end{cases}}\Rightarrow\orbr{\begin{cases}x=-3\\x=11\end{cases}}\)

=5

nhanh lên nha !!

2 x 1 +3

=2+3

=5

2x1+3=5

tk mk nha

x+5 chia hết x-2

(x+5) - (x-2) chia hết x-2

x+5 - x+2 chia hết x-2

7 chia hết x-2

x-2 thuộc Ư(7)={-1;1;-7;7}

x thuộc {1;3;-5;9}

100 mk nhanh 

10 x 10 = 100

10 x 10 = ?

10 x 10 = 100 

sorry bn nha ! mk hết lượt rồi !

x+y=27

vì x=2y

\(\Rightarrow\)2y+y=27

        y(2+1)=27

        y.3     =27

       y         =27:3

       y         =9

x+9=27

x    =27-9

x    =18

Vậy y=9 và x=18

y là:

27 : (1 + 2) = 9

x là:

27 - 9 = 18

ĐS: x: 18

       y: 9

Theo bài ra ta có :

x + y = 27

y + y x 2 = 27

y x 1 + y x 2 = 27

 y x ( 1 + 2 )  = 27

       y x 3       = 27

             y       = 27 ÷ 3

             y       = 9

\(\Rightarrow\)x = 2 × 9 = 18