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

a) ĐKXĐ: 

\(x^2-1\ne0\Leftrightarrow x\ne\pm1\)

b) \(A=\dfrac{x^2-2x+1}{x^2-1}\)

\(A=\dfrac{x^2-2\cdot x\cdot1+1^2}{x^2-1^2}\)

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

\(A=\dfrac{x-1}{x+1}\)

c) Thay x = 3 vào A ta có:

\(A=\dfrac{3-1}{3+1}=\dfrac{2}{4}=\dfrac{1}{2}\)

a) ĐKXĐ: 

\(9x^2-y^2\ne0\Leftrightarrow\left(3x\right)^2-y^2\ne0\Leftrightarrow\left(3x-y\right)\left(3x+y\right)\ne0\)

\(\Leftrightarrow3x\ne\pm y\) 

b) \(B=\dfrac{6x-2y}{9x^2-y^2}\)

\(B=\dfrac{2\cdot3x-2y}{\left(3x\right)^2-y^2}\)

\(B=\dfrac{2\left(3x-y\right)}{\left(3x+y\right)\left(3x-y\right)}\)

\(B=\dfrac{2}{3x+y}\)

Thay x = 1 và \(y=\dfrac{1}{2}\) và B ta có:

\(B=\dfrac{2}{3\cdot1+\dfrac{1}{2}}=\dfrac{2}{3+\dfrac{1}{2}}=\dfrac{2}{\dfrac{7}{2}}=\dfrac{4}{7}\)

Bài 1 : 

\(\left(x-2\right)^2-\left(x-3^2\right)=\left(x-2\right)^2-\left(x-9\right)\)

\(=x^2-4x+4-x+9=x^2-5x+13\)

Bài 2 : 

a, \(P=\frac{1-4x^2}{4x^2-4x+1}=\frac{\left(1-2x\right)\left(2x+1\right)}{\left(2x-1\right)^2}\)

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

b, Thay x = -4 ta được : 

\(\frac{-2.\left(-4\right)-1}{2.\left(-4\right)-1}=\frac{8-1}{-8-1}=-\frac{7}{9}\)

\(\dfrac{x^5+x^3+x^2+1}{x^3+x^2+x+1}=\dfrac{x^3\left(x^2+1\right)+\left(x^2+1\right)}{x^2\left(x+1\right)+\left(x+1\right)}\)

= \(\dfrac{\left(x^3+1\right)\left(x^2+1\right)}{\left(x^2+1\right)\left(x+1\right)}=\dfrac{\left(x+1\right)\left(x^2-x+1\right)}{x+1}=x^2-x+1\)

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

`(x^5+x^3+x^2+1)/(x^3+x^2+x+1)(x ne -1)`

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

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

`=(x^3+1)/(x+1)`

`=((x+1)(x^2-x+1))/(x+1)`

`=x^2-x+1`

Câu này  cô làm rồi em nhá, em xem phần câu hỏi của tôi ý

\(M=\dfrac{x^2}{x^2-3x}\left(x\ne0;x\ne3\right)\\ M=\dfrac{x^2}{x\left(x-3\right)}\\ M=\dfrac{x}{x-3}\)

\(N=\dfrac{x}{x+1}+\dfrac{3x+1}{x^2-1}\left(x\ne\pm1\right)\\ N=\dfrac{x-1+3x+1}{\left(x+1\right)\left(x-1\right)}=\dfrac{4x}{\left(x+1\right)\left(x-1\right)}\)

a) M=\(\dfrac{x^2}{x^2-3x}\)=\(\dfrac{x.x}{x\left(x-3\right)}\)=\(\dfrac{x}{x-3}\)

b)\(\dfrac{x}{x+1}+\dfrac{3x+1}{x^2-1}\)=\(\dfrac{2x^2+4x+1}{x^3+x^2}\)

\(M=\dfrac{x^2}{x^2-3x}=\dfrac{x}{x-3}\)

\(N=\dfrac{x}{x+1}+\dfrac{3x+1}{x^2-1}=\dfrac{x^2-x+3x+1}{\left(x+1\right)\left(x-1\right)}=\dfrac{x+1}{x-1}\)

alo chào bn ạ,bn kb vs mình nha mình ib rồi ạ

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

Q = \(\dfrac{1+x^4+x^8+...+x^{2020}}{1+x^2+...+x^{2022}}\)

Đặt A = 1 + \(x^4\) + \(x^8\) +...+ \(x^{2020}\)

Đặt B = 1 + \(x^2\) + ...+ \(x^{2022}\)

Thì Q = \(\dfrac{A}{B}\) 

A              = 1 + \(x^4\) + \(x^8\) + ...+ \(x^{2020}\)

A.\(x^4\)         =       \(x^4\) + \(x^8\) +....+ \(x^{2020}\) + \(x^{2024}\)

A.\(x^4\) - A    = \(x^{2024}\) - 1

A              = \(\dfrac{x^{2024}-1}{x^4-1}\) 

B             = 1 + \(x^2\) + \(x^4\) +...+ \(x^{2020}\) + \(x^{2022}\) 

B.\(x^2\)        =       \(x^2\) + \(x^4\) +...+ \(x^{2020}\) + \(x^{2022}\) + \(x^{2024}\)

B\(x^2\) - B   =       \(x^{2024}\) - 1

B             = \(\dfrac{x^{2024}-1}{x^2-1}\)

Q = \(\dfrac{\dfrac{x^{2024}-1}{x^4-1}}{\dfrac{x^{2024}-1}{x^2-1}}\)

Q  = \(\dfrac{x^{2024}-1}{x^4-1}\) \(\times\)\(\dfrac{x^2-1}{x^{2024}-1}\)

Q  = \(\dfrac{1}{x^2+1}\)

\(=\dfrac{1-x}{xy\left(x-1\right)}=\dfrac{-1}{xy}\)