a: \(=\dfrac{x^2+x-2x+2-2}{\left(x-1\right)\left(x+1\right)}=\dfrac{x^2-x}{\left(x-1\right)\left(x+1\right)}=\dfrac{x}{x+1}\)

a:  để \(\dfrac{4}{x}>\dfrac{4}{5}\\ \Rightarrow x< 5\)

mà x là các số tự nhiên 

\(\Rightarrow x\in\left\{1;2;3;4\right\}\)

b: để \(\dfrac{1}{9}< \dfrac{x}{9}< \dfrac{4}{9}th\text{ì}1< x< 4\\ \Rightarrow x\in\left\{2;3\right\}\)

A) x>5 => x=1,x=2,x=3,x=4 do hai tử bằng nhau thì phân số nào có mẫu nhỏ hơn sẽ lớn hơn

B) x=2 hoặc x= 3 

C) x=7

\(a,\Rightarrow x-2=8\\ \Rightarrow x=10\\ b,\Rightarrow x+12-17=20\\ \Rightarrow x-5=20\\ \Rightarrow x=25\\ c,\Rightarrow11-\left(4x+5\right):3=4\\ \Rightarrow\left(4x+5\right):3=7\\ \Rightarrow4x+5=21\\ \Rightarrow x=4\\ d,\Rightarrow\left(35:x+3\right)\cdot17=136\\ \Rightarrow35:x+3=8\\ \Rightarrow35:x=5\\ \Rightarrow x=7\\ e,\Rightarrow41-\left(2x-5\right)=720:8\cdot5=180\\ \Rightarrow2x-5=-139\\ \Rightarrow2x=-134\\ \Rightarrow x=-67\)

\(2,\\ a,\Rightarrow x^2=4^3:16=64:16=4=2^2=\left(-2\right)^2\\ \Rightarrow\left[{}\begin{matrix}x=2\\x=-2\end{matrix}\right.\\ b,\Rightarrow\left(x-1\right)^2=9=3^2=\left(-3\right)^2\\ \Rightarrow\left[{}\begin{matrix}x-1=3\\x-1=-3\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=4\\x=-2\end{matrix}\right.\\ c,\Rightarrow\left(3x-7\right)^5=2^5\\ \Rightarrow3x-7=2\\ \Rightarrow3x=9\Rightarrow x=3\)

a: góc ASB=1/2*180=90 độ=góc ABM

b: ON vuông góc AS

BS vuông góc SA

=>ON//BS

c: góc OIM+góc OBM=180 độ

=>OIMB nội tiếp

c) \(x-\dfrac{10}{3}=\dfrac{7}{15}\cdot\dfrac{3}{5}\)

    \(x-\dfrac{10}{3}=\dfrac{7}{25}\)

    \(x=\dfrac{7}{25}+\dfrac{10}{3}\)

    \(x=\dfrac{271}{75}\)

d) \(x+\dfrac{3}{22}=\dfrac{27}{121}\div\dfrac{9}{11}\)

    \(x+\dfrac{3}{22}=\dfrac{3}{11}\)

    \(x=\dfrac{3}{11}-\dfrac{3}{22}\)

    \(x\)   \(=\dfrac{3}{22}\)

e) \(\dfrac{8}{23}\div\dfrac{24}{46}-x=\dfrac{1}{3}\)

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

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

                      \(x=\dfrac{1}{3}\)

f) \(1-x=\dfrac{49}{65}\cdot\dfrac{5}{7}\)

   \(1-x=\dfrac{7}{13}\)

         \(x=1-\dfrac{7}{13}\)

         \(x=\dfrac{6}{13}\)

1 because

2 as long as

3 although

4 so that

5 although

6 even if

7 until

8 while

9 because

10 Although