b: Gọi A là Tọa độ giao điểm của hàm số với trục tung

=>Tọa độ của A là:

\(\left\{{}\begin{matrix}x=0\\y=\left(m-2\right)\cdot0+m+3=m+3\end{matrix}\right.\)

Gọi B là Tọa độ giao điểm của hàm số với trục hoành

=>Tọa độ của B là:

\(\left\{{}\begin{matrix}\left(m-2\right)\cdot x+m+3=0\\y=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{-m-3}{m-2}\\y=0\end{matrix}\right.\)

Theo đề, ta có: \(\left|m+3\right|=\left|\dfrac{-m-3}{m-2}\right|\)

\(\Leftrightarrow\left[{}\begin{matrix}m+3=\dfrac{-m-3}{m-2}\\m+3=\dfrac{m+3}{m-2}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}m^2+m-6+m+3=0\\m^2+m-6-m-3=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}\left(m+3\right)\left(m-1\right)=0\\\left(m+3\right)\left(m-3\right)=0\end{matrix}\right.\Leftrightarrow m\in\left\{-3;1;3\right\}\)

c: Ta có: \(\left(x-3\right)^3-\left(x^3-27\right)+9\left(x+1\right)^2=15\)

\(\Leftrightarrow x^3-9x^2+27x-27-x^3+27+9\left(x^2+2x+1\right)=15\)

\(\Leftrightarrow-9x^2+27x+9x^2+18x+9=15\)

\(\Leftrightarrow45x=6\)

hay \(x=\dfrac{2}{15}\)

d: Ta có: \(x\left(x-5\right)\left(x+5\right)-\left(x^3+8\right)=3\)

\(\Leftrightarrow x^3-25x-x^3-8=3\)

\(\Leftrightarrow-25x=11\)

hay \(x=-\dfrac{11}{25}\)

1.Yes, they do

2..Yes, it is

3.People buy fruits and flowers from the market and decorate their house

4.People visit their family and friends

1 friendly

 2 creative

3 boring

4 funny

5 sensitive

6  outgoing

7 lazy

8 impatient

9 active

10 quiet

a) ĐKXĐ: \(\left\{{}\begin{matrix}2x+3\ne0\\2x+1\ne0\\\left(2x+3\right)\left(2x+1\right)\ne0\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}x\ne-\dfrac{3}{2}\\x\ne-\dfrac{1}{2}\\\left(2x+3\right)\left(2x+1\right)\ne0\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}x\ne-\dfrac{3}{2}\\x\ne-\dfrac{1}{2}\end{matrix}\right.\)

b) \(\Rightarrow P=\dfrac{2\left(2x+1\right)+3\left(2x+3\right)-6x-5}{\left(2x+3\right)\left(2x+1\right)}\)

\(\Rightarrow P=\dfrac{4x+2+6x+9-6x-5}{\left(2x+3\right)\left(2x+1\right)}\)

\(\Rightarrow P=\dfrac{4x+6}{\left(2x+3\right)\left(2x+1\right)}\)

\(\Rightarrow P=\dfrac{2\left(2x+3\right)}{\left(2x+3\right)\left(2x+1\right)}\)

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

c) \(P=-1\Rightarrow\dfrac{2}{2x+1}=-1\\ \Rightarrow2=-2x-1\\ \Rightarrow2x=-3\\ \Rightarrow x=-\dfrac{3}{2}\)