Question

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

Answer 1

\(\frac{x+2}{5}=\frac{1}{x-2}\left(ĐK:x\ne2\right)\)

\(\Leftrightarrow\left(x+2\right)\left(x-2\right)=5\)

\(\Leftrightarrow x^2-4=5\)

\(\Leftrightarrow x^2=9\)

\(\Leftrightarrow\left[\begin{array}{nghiempt}x=\sqrt{9}\\x=-\sqrt{9}\end{array}\right.\)

Answer 2

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

=> (x + 2).(x - 2) = 5

Mà x + 2 > x - 2

=> \(\left[\begin{array}{nghiempt}x+2=5;x-2=1\\x+2=-1;x-2=-5\end{array}\right.\)

+ Với \(\begin{cases}x+2=5\\x-2=1\end{cases}\)\(\Rightarrow x=3\)

+ Với \(\begin{cases}x+2=-1\\x-2=-5\end{cases}\)\(\Rightarrow x=-3\)

Vậy \(\left[\begin{array}{nghiempt}x=3\\x=-3\end{array}\right.\)

Answer 3

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

\(\Rightarrow\left(x+2\right)\left(x-2\right)=5.1\)

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

\(\Rightarrow x^2=5-4=1\)

\(\Rightarrow x=1\)

Answer 4

thôi mệt quá, sau câu nào cũng sai.