Rut gon:  S= 2+2^2+2^3+.................. + 2^100
              \(\Rightarrow\) 2S= 2 ( 2+2^2+2^3+.................. + 2^100 )
              2S= 2^2+2^3+.................. + 2^101

              2S-S= 2^101-2

1) Nhóm 4 số hạng liên tiếp vào

2) Chữ số tận cùng là 2

3) Rút gọn S = 2¹⁰¹ - 2

Đề sai ạ ! Sửa nhé :

\(S=\left(\frac{2+x}{2-x}+\frac{4x^2}{x^2-4}-\frac{2-x}{2+x}\right):\frac{x^3-4x}{2x^2-x^3}\)

\(\Leftrightarrow S=\left(\frac{-\left(x+2\right)}{x-2}+\frac{4x^2}{\left(x-2\right)\left(x+2\right)}+\frac{x-2}{x+2}\right):\frac{x\left(x^2-4\right)}{x^2\left(2-x\right)}\)

\(\Leftrightarrow S=\left(\frac{-\left(x+2\right)^2+4x^2+\left(x-2\right)^2}{\left(x-2\right)\left(x+2\right)}\right):\frac{\left(x-2\right)\left(x+2\right)}{-x\left(x-2\right)}\)

\(\Leftrightarrow S=\frac{-x^2-4x-4+4x^2+x^2-4x+4}{\left(x+2\right)\left(x-2\right)}.\frac{-x}{\left(x+2\right)}\)

\(\Leftrightarrow S=\frac{-x\left(4x^2-8x\right)}{\left(x+2\right)^2\left(x-2\right)}\)

\(\Leftrightarrow S=\frac{-4x^2\left(x-2\right)}{\left(x+2\right)^2\left(x-2\right)}\)

\(\Leftrightarrow S=\frac{-4x^2}{\left(x+2\right)^2}\)

P/s : nếu làm theo đề của bạn, sẽ ra kq dài... Nên mik tiện sửa, còn nếu đề bạn đúng rồi thì mik sẽ làm lại ạ !

mình nhầm tí nhé bạn

\(\frac{x^2-3x}{2x^2-x^3}\)

P/s : Làm theo đề đã sửa ạ !

\(S=\left(\frac{2+x}{2-x}+\frac{4x^2}{x^2-4}-\frac{2-x}{2+x}\right):\frac{x^2-3x}{2x^2-x^3}\)

\(\Leftrightarrow S=\left(\frac{-\left(x+2\right)}{x-2}+\frac{4x^2}{\left(x-2\right)\left(x+2\right)}+\frac{x-2}{2+x}\right):\frac{x\left(x-3\right)}{-x^2\left(x-2\right)}\)

\(\Leftrightarrow S=\frac{-\left(x+2\right)^2+4x^2+\left(x-2\right)^2}{\left(x-2\right)\left(x+2\right)}.\frac{-x\left(x-2\right)}{\left(x-3\right)}\)

\(\Leftrightarrow S=\frac{-x\left(-x^2-4x-4+4x^2+x^2-4x+4\right)\left(x-2\right)}{\left(x-2\right)\left(x+2\right)\left(x-3\right)}.\)

\(\Leftrightarrow S=\frac{-x\left(4x^2-8x\right)}{\left(x+2\right)\left(x-3\right)}\)

\(\Leftrightarrow S=\frac{4x^2\left(2-x\right)}{\left(x+2\right)\left(x-3\right)}\)

a: \(\dfrac{4\cdot5+4\cdot11}{8\cdot7+4\cdot3}=\dfrac{4\cdot16}{4\left(2\cdot7+3\right)}=\dfrac{16}{17}=\dfrac{11088}{11781}\)

\(\dfrac{-15\cdot8+10\cdot7}{5\cdot6+20\cdot3}=\dfrac{-120+170}{30+60}=\dfrac{50}{90}=\dfrac{5}{9}=\dfrac{6545}{11781}\)

\(\dfrac{2^4\cdot5^2\cdot7}{2^3\cdot5\cdot7^2\cdot11}=2\cdot5\cdot\dfrac{1}{77}=\dfrac{10}{77}=\dfrac{1530}{11781}\)