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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\(P=\dfrac{2}{x^2+x+1}\)

a, \(\dfrac{x+3}{3x-3}\) + \(\dfrac{2-x}{4x-4}\) 

đkxđ: \(\left\{{}\begin{matrix}3x-3\ne0\\4x-4\ne0\end{matrix}\right.\) ⇒ \(\left\{{}\begin{matrix}3.\left(x-1\right)\ne0\\4.\left(x-1\right)\ne0\end{matrix}\right.\) ⇒ \(\left\{{}\begin{matrix}x-1\ne0\\x-1\ne0\end{matrix}\right.\) ⇒ \(x\) ≠1

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

A = \(\dfrac{x+3}{3.\left(x-1\right)}\) + \(\dfrac{2-x}{4.\left(x-1\right)}\) 

A = \(\dfrac{4.\left(x+3\right)}{4.3.\left(x-1\right)}\) + \(\dfrac{3.\left(2-x\right)}{3.4.\left(x-1\right)}\)

A = \(\dfrac{4x+12}{12\left(x-1\right)}\) + \(\dfrac{6-3x}{12\left(x-1\right)}\)

A = \(\dfrac{4x+12+6-3x}{12\left(x-1\right)}\)

A = \(\dfrac{\left(4x-3x\right)+\left(12+6\right)}{12\left(x-1\right)}\)

A = \(\dfrac{x+18}{12.\left(x-1\right)}\)

b, \(\dfrac{3}{x+2}-\dfrac{6}{x-1}\) 

Đkxđ: \(\left\{{}\begin{matrix}x+2\ne0\\x-1\ne0\end{matrix}\right.\) ⇒ \(\left\{{}\begin{matrix}x\ne-2\\x\ne1\end{matrix}\right.\)

B = \(\dfrac{3}{x+2}\) - \(\dfrac{6}{x-1}\)

B = \(\dfrac{3.\left(x-1\right)}{\left(x+2\right)\left(x-1\right)}\) - \(\dfrac{6.\left(x+2\right)}{\left(x-1\right)\left(x+2\right)}\)

B = \(\dfrac{3x-3}{\left(x+2\right)\left(x-1\right)}\) - \(\dfrac{6x+12}{\left(x-1\right)\left(x+2\right)}\)

B = \(\dfrac{3x-3-\left(6x+12\right)}{\left(x+2\right)\left(x-1\right)}\)

B = \(\dfrac{3x-3-6x-12}{\left(x+2\right)\left(x-1\right)}\)

B = \(\dfrac{\left(3x-6x\right)-\left(12+3\right)}{\left(x+2\right)\left(x-1\right)}\)

B = \(\dfrac{-3x-15}{\left(x+2\right)\left(x-1\right)}\)

and

I have to tidy my bedroom because I have to dust the living room.

   2\(x^2\)y² - 6\(\sqrt{2}\)\(xy\) + 9

= (\(\sqrt{2}\).\(x.y\))² - 2.\(\sqrt{2}\)\(xy\).3 + 3²

= (\(\sqrt{2}\)\(xy\)  - 3)²

\(M_{H_2}=1.2=2g/mol\\ M_{O_2}=16.2=32g/mol\\ M_{CO_2}=12+16.2=44g/mol\\ M_{Al_2O_3}=27.2+16.3=102g/mol\\ M_{Fe}=56g/mol\\ M_{Mg}=24g/mol\)

a) PTHH \(S+O_2\underrightarrow{t^o}SO_2\)

b) Khí SO₂ chính là chất làm cho chuột chết. Hợp chất này tên là lưu huỳnh đi-ô-xít (tên Tiếng Anh là sulfur dioxide). Đây là một oxit axit. 

As a responsible member of my family, I always strive to contribute and assist in various ways. I take on household chores such as cleaning, organizing, and tidying up the living spaces. Additionally, I help with grocery shopping and meal preparation, ensuring that everyone's dietary needs are met. I also assist my siblings with their homework and offer guidance whenever they need it. Furthermore, I actively participate in family discussions and decision-making processes, providing my input and suggestions. By actively engaging in these activities, I aim to alleviate the workload of my family members and create a harmonious and supportive environment for everyone.

I always try to be a helpful member of my family by doing various tasks around the house. I assist with household chores such as cleaning, laundry, and cooking. Additionally, I help my younger siblings with their homework and school projects. I am mindful of our family's budget by conserving energy and reducing waste. I also help with grocery shopping and finding the best deals. Being a responsible and helpful member of my family is important to me, and I will continue to do my part to make our home run smoothly.

a, (a² + b²).(c² + d²)

=   a².c² + a².d² + b².c² + b².d² (1)

(ac + bd)² + (ad - bc)²

= a².c² + 2abcd + b².d² + a².d² - 2abcd + b².c²

= a².c² + b².d² + a².d² + b².c²  (2)

Kết hợp (1) và (2) ta có:

(a²+b²).(c²+d²) = (ac + bd)² + (ad - bc)² (đpcm)

Bài 4 ý 2,

           (a + b + c)³

= (a+b)³ + 3(a+b)².c + 3.(a+b).c² + c³

= a³ + 3a²b+3ab² + b³ + 3.(a+b).[ (a + b).c + c²] + c³

= a³ + 3a²b + 3ab² + b³   +   3(a+b)[ac + bc + c²] + c³

= a³+b³+ c³ + 3ab.(a + b) + 3.(a + b)[ac + bc + c²] 

= a³ + b³ + c³ + 3.(a + b).(ab + ac + bc + c²]

= a³ + b³ + c³ + 3.(a + b).[(ab + bc) + (ac + c²)]

= a³ + b³ + c³ + 3.(a + b).[b.(a + c) + c.(a + c)]

= a³ + b³ + c³ + 3.(a + b).(a+c).(b+c) (đpcm)