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

\(\Leftrightarrow\frac{2}{x\left(x-2\right)}+\frac{1}{x}-\frac{x+2}{x-2}=0\)

\(\Leftrightarrow\frac{2}{x\left(x-2\right)}+\frac{x-2}{x\left(x-2\right)}+\frac{x\left(x+2\right)}{x\left(x-2\right)}=0\)

\(\Leftrightarrow\frac{2+x-2+x^2+2x}{x\left(x-2\right)}=0\)

\(\Leftrightarrow\frac{x^2+3x}{x\left(x-2\right)}=0\)

\(\Leftrightarrow\frac{x\left(x+3\right)}{x\left(x-2\right)}=0\)

\(\Leftrightarrow\frac{x+3}{x-2}=0\)

\(\Rightarrow x+3=0\left(x-2\ne0\right)\)

\(\Leftrightarrow x=-3\)

\(\frac{3x^2+7x-10}{x}=0\)

\(3x^2+7x-10=0\)

\(3x^2-3x+10x-10=0\)

\(3x\left(x-1\right)+10\left(x-1\right)=0\)

\(\left(3x+10\right)\left(x-1\right)=0\)

\(\Rightarrow\orbr{\begin{cases}3x+10=0\\x-1=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=\frac{-10}{3}\\x=1\end{cases}}\)

\(ĐKXĐ:\)\(x\ne0\)

       \(\frac{3x^2+7x-10}{x}=0\)

\(\Rightarrow\)\(3x^2+7x-10=0\)

\(\Leftrightarrow\)\(\left(x-1\right)\left(3x+10\right)=0\)

\(\Leftrightarrow\)\(\orbr{\begin{cases}x-1=0\\3x+10=0\end{cases}}\)

\(\Leftrightarrow\)\(\orbr{\begin{cases}x=1\left(TMĐKXĐ\right)\\x=-\frac{10}{3}\left(TMĐKXĐ\right)\end{cases}}\)

Vậy...

a/ x=3 b/ x=-2/9 c/ x=4 d/ x=2

a) x=3

b)x=\(\dfrac{-2}{9}\)

c)x=4

d)x=2

chúc bạn học tốt

\(\frac{x+2}{x+3}-\frac{x+1}{x-1}=\frac{4}{\left(x-1\right)\left(x+3\right)}\left(x\ne-3;x\ne1\right)\)

\(\Leftrightarrow\frac{x+2}{x+3}-\frac{x+1}{x-1}-\frac{4}{\left(x-1\right)\left(x+3\right)}=0\)

\(\Leftrightarrow\frac{\left(x+2\right)\left(x-1\right)}{\left(x+3\right)\left(x-1\right)}-\frac{\left(x+1\right)\left(x+3\right)}{\left(x-1\right)\left(x+3\right)}-\frac{4}{\left(x-1\right)\left(x+3\right)}=0\)

\(\Leftrightarrow\frac{x^2+x-2}{\left(x+3\right)\left(x-1\right)}-\frac{x^2+4x+3}{\left(x-1\right)\left(x+3\right)}-\frac{4}{\left(x-1\right)\left(x+3\right)}=0\)

\(\Leftrightarrow\frac{x^2+x-2-x^2-4x-3-4}{\left(x-1\right)\left(x+3\right)}=0\)

\(\Leftrightarrow\frac{-3x-9}{\left(x-1\right)\left(x+3\right)}=0\)

\(\Leftrightarrow\frac{-3\left(x+3\right)}{\left(x-1\right)\left(x+3\right)}=0\)

\(\Leftrightarrow\frac{-3}{x-1}=0\)

=> PT vô nghiệm

a)\(\frac{3}{7}x\)-1=\(\frac{1}{7}x\)(3x-7)                                                                                                                                                                  <=>\(\frac{3}{7}x-1\)=\(\frac{3}{7}x^2-1\)<=>\(\frac{3}{7}x\)-\(\frac{3}{7}x^2\)=0<=>\(\frac{3}{7}x\)=\(\frac{3}{7}x^2\)                                                                                     <=>\(\frac{\frac{3}{7}}{\frac{3}{7}}\)=\(\frac{x^2}{x}\)^<=>\(1=x\)                                                                                                                                                                                          

\(a, 2x^2 + 5x + 10 = x^2 + 5x - 11\)

\(<=> x^2 + 21 = 0 \)

\(Do x^2 + 21 > 0\)

=> Pt vô nghiệm

\(b, 2x^2 - 6x + 7 = 0\)

\(<=> 2(x^2 - 3x+7/2)=0\)

\(<=> (x-3/2)^2 +7/4 = 0 \)

Tương tự như trên thì pt vô nghiệm

\(c, |x^2 + 3x+20| + |x-3| = 0\)

Ta có : \(|x^2 + 3x+20| = |(x+3/2)^2 + 17,75| > 0\)

 \(=> |x^2 + 3x+20| + |x-3| > 0\)

=> Pt vô nghiệm

Đặt \(u=x^2-x\)

Phương trình trở thành \(u^2-4u+4=0\)

\(\Leftrightarrow\left(u-2\right)^2=0\)

\(\Leftrightarrow u-2=0\)

\(\Rightarrow x^2-x=2\)

\(\Rightarrow x^2-x-2=0\)

Ta có \(\Delta=1^2+4.2=9,\sqrt{\Delta}=3\)

\(\Rightarrow\orbr{\begin{cases}x=\frac{1+3}{2}=2\\x=\frac{1-3}{2}=-1\end{cases}}\)

Đặt \(2x+1=w\)

Phương trình trở thành \(w^2-w=2\)

\(\Rightarrow\orbr{\begin{cases}w=2\\w=-1\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}2x+1=2\\2x+1=-1\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}x=\frac{1}{2}\\x=-1\end{cases}}\)