\(ĐKXĐ:\)   \(\forall x\in Z\)

              \(\frac{x^2}{x^2+2x+2}+\frac{x^2}{x^2-2x+2}-\frac{4\left(x^2-5\right)}{x^4+4}=\frac{322}{65}\)

\(\Leftrightarrow\)\(\frac{x^2\left(x^2-2x+2\right)}{\left(x^2+2x+2\right)\left(x^2-2x+2\right)}+\frac{x^2\left(x^2+2x+2\right)}{\left(x^2-2x+2\right)\left(x^2+2x+2\right)}-\frac{4\left(x^2-5\right)}{\left(x^2-2x+2\right)\left(x^2+2x+2\right)}=\frac{322}{65}\)

\(\Leftrightarrow\)\(\frac{x^4-2x^3+2x^2+x^4+2x^3+2x^2-4x^2+20}{\left(x^2-2x+2\right)\left(x^2+2x+2\right)}=\frac{322}{65}\)

\(\Leftrightarrow\)\(\frac{2x^4+10}{x^4+4}=\frac{322}{65}\)

\(\Rightarrow\)\(65\left(2x^4+10\right)=322\left(x^4+4\right)\)

\(\Leftrightarrow\)\(130x^4+650=322x^4+1288\)

\(\Leftrightarrow\)\(192x^4=-638\)  (vô lý)

Vậy pt vô nghiệm

P/S:mk lm bừa thôi, đúng thì you tham khảo, sai thì báo mk biết nha

a/ \(\frac{x^2+2x+1}{x^2+2x+2}+\frac{x^2+2x+2}{x^2+2x+3}=\frac{7}{6}\)

<=> \(\frac{\left(x+1\right)^2}{\left(x+1\right)^2+1}+\frac{\left(x+1\right)^2+1}{\left(x+1\right)^2+2}=\frac{7}{6}\left(1\right)\)

đặt \(\left(x+1\right)^2=a\left(a>0\right)\)

=> \(\left(1\right)\)<=> \(\frac{a}{a+1}+\frac{a+1}{a+2}=\frac{7}{6}\)

<=> \(\frac{a\left(a+2\right)+\left(a+1\right)^2}{\left(a+1\right)\left(a+2\right)}=\frac{7}{6}\)

<=> \(\frac{2a^2+4a+1}{a^2+3a+2}=\frac{7}{6}\)

<=> \(6\left(2a^2+4a+1\right)=7\left(a^2+3a+2\right)\)

<=> \(5a^2+3a-8=0\)

<=> \(5a^2-5a+8a-8=0\)

<=>  \(\left(5a+8\right)\left(a-1\right)=0\)

<=> \(a=\frac{-8}{5}\left(h\right)a=1\)

mà \(a>0\)

=> \(a=1\)

=> \(\left(x+1\right)^2=1\)

=> \(x+1=1\left(h\right)x+1=-1\)

=> \(x=0\left(h\right)x=-2\)

vậy  ......

chúc bn học tốt

Xét x = 0 và x = -2 , thay vào ta được \(VT=VP\)

Xét x > 0 : 

\(VT=\frac{x^2+2x+1}{x^2+2x+2}+\frac{x^2+2x+2}{x^2+2x+3}=1-\frac{1}{x^2+2x+2}+1-\frac{1}{x^2+2x+3}\)

\(=2-\left(\frac{1}{x^2+2x+2}+\frac{1}{x^2+2x+3}\right)>2-\left(\frac{1}{2}+\frac{1}{3}\right)>\frac{7}{6}=VP\) ( loại ) 

Xét x < -2 : 

\(VT=2-\left(\frac{1}{x\left(x+2\right)+2}+\frac{1}{x\left(x+2\right)+3}\right)>2-\left(\frac{1}{2}+\frac{1}{3}\right)=\frac{7}{6}=VP\) ( loại ) 

Xét -2 < x < 0 : 

\(VT=2-\left(\frac{1}{x^2+2x+2}+\frac{1}{x^2+2x+3}\right)>2-\left(\frac{1}{-2}+1\right)=\frac{3}{2}>\frac{7}{6}=VP\) ( loại ) 

Vậy ... 

\(a,ĐKXĐ:x\ne\pm\frac{1}{2}\)

Ta có: \(\frac{2}{2x+1}-\frac{3}{2x-1}=\frac{4}{4x^2-1}\)

\(\Leftrightarrow2\left(2x-1\right)-3\left(2x+1\right)=4\)

\(\Leftrightarrow4x-2-6x-3=4\)

\(\Leftrightarrow-2x=9\)

\(\Leftrightarrow x=-\frac{9}{2}\)(Tm ĐKXĐ)

Vậy pt có nghiệm duy nhất \(x=-\frac{9}{2}\)

\(b,ĐKXĐ:x\ne\pm1;-3\)

Ta có: \(\frac{2x}{x+1}+\frac{18}{x^2+2x-3}=\frac{2x-5}{x+3}\)

\(\Leftrightarrow\frac{2x}{x+1}+\frac{18}{\left(x-1\right)\left(x+3\right)}=\frac{2x-5}{x+3}\)

\(\Leftrightarrow2x\left(x-1\right)\left(x+3\right)+18\left(x+1\right)=\left(2x-5\right)\left(x-1\right)\left(x+1\right)\)

\(\Leftrightarrow2x\left(x^2+2x-3\right)+18x+18=\left(2x-5\right)\left(x^2-1\right)\)

\(\Leftrightarrow2x^3+4x^2-6x+18x+18=2x^3-2x-5x^2+5\)

\(\Leftrightarrow9x^2+14x+13=0\)

\(\Leftrightarrow\left(9x^2+14x+\frac{49}{9}\right)+\frac{68}{9}=0\)

\(\Leftrightarrow\left(3x+\frac{7}{3}\right)^2+\frac{68}{9}=0\)

Pt vô nghiệm 

\(c,ĐKXĐ:x\ne1\)

Ta có: \(\frac{1}{x-1}+\frac{2x^2-5}{x^3-1}=\frac{4}{x^2+x+1}\)

\(\Leftrightarrow x^2+x+1+2x^2-5=x-1\)

\(\Leftrightarrow3x^2=3\)

\(\Leftrightarrow x^2=1\)

\(\Leftrightarrow x=\pm1\)

Kết hợp vs ĐKXĐ được x = -1

Vậy pt có nghiệm duy nhất x = -1

làm lần lượt nha(bài nào k bt bỏ qua)

\(a,\frac{2}{2x+1}-\frac{3}{2x-1}=\frac{4}{4x^2-1}\)

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

\(\Rightarrow-2x-5=4\)

\(\Rightarrow-2x=9\)

\(\Rightarrow x=\frac{9}{-2}\)

a) \(\frac{x-1}{2}+\frac{x-2}{3}+\frac{x-3}{4}=\frac{x-4}{5}+\frac{x-5}{6}\)

\(\left(\frac{x-1}{2}+1\right)+\left(\frac{x-2}{3}+3\right)+\left(\frac{x-3}{4}+1\right)=\left(\frac{x-4}{5}+1\right)+\left(\frac{x-5}{6}+1\right)\)

\(\frac{x-1}{2}+\frac{x-1}{3}+\frac{x-1}{4}=\frac{x-1}{5}+\frac{x-1}{6}\)

\(\left(x-1\right)\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}\right)\)=0

\(x-1=0\)

\(x=1\)

các bạn giúp mình với. cảm ơn 

giúp mình với

a,\(\frac{13}{\left(x-3\right)\left(2x+7\right)}+\frac{1}{2x+7}=\frac{6}{x^2-9}\)\(\Leftrightarrow\frac{13\left(x+3\right)}{\left(x^2-9\right)\left(2x+7\right)}+\frac{x^2-9}{\left(x^2-9\right)\left(2x+7\right)}-\frac{6\left(2x+7\right)}{\left(x^2-9\right)\left(2x+7\right)}=0\)

\(\Leftrightarrow x+x^2-12=0\Leftrightarrow\orbr{\begin{cases}x=-4\\x=3\end{cases}}\)

b,\(\frac{x-3}{x-5}+\frac{1}{x}=\frac{x+5}{x\left(x-5\right)}\Leftrightarrow\frac{x\left(x-3\right)}{x\left(x-5\right)}+\frac{x-5}{x\left(x-5\right)}-\frac{x+5}{x\left(x-5\right)}=0\)

\(\Leftrightarrow x^2-3x-10=0\Rightarrow\orbr{\begin{cases}x=5\left(L\right)\\x=-2\end{cases}}\)

c,\(\frac{1}{x+2}+\frac{1}{x\left(x-2\right)}-\frac{8}{x\left(x^2-4\right)}=0\)\(\Leftrightarrow\frac{x\left(x-2\right)}{x\left(x^2-4\right)}+\frac{x+2}{x\left(x^2-4\right)}-\frac{8}{x\left(x^2-4\right)}=0\)

\(\Leftrightarrow x^2-x-6=0\Rightarrow\orbr{\begin{cases}x=3\\x=-2\left(L\right)\end{cases}}\)

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

\(\Leftrightarrow-x^2-5x-10=0\)(vô nghiệm)

\(\)