Question

Tìm x trong tỉ lệ thức :

a) x+2/5=1/x-2 (x khác 2 )

b) 3/x-4=x+4/3 (x khác 4 )

c) x+2/2=1/1-x (x khác 1 )

Answer 1

a, \(\frac{x+2}{5}=\frac{1}{x-2}\Rightarrow\left(x+2\right)\left(x-2\right)=5\Rightarrow x^2-2x+2x-4=5\Rightarrow x^2=9\Rightarrow x=\pm3\)

b, \(\frac{3}{x-4}=\frac{x+4}{3}\Rightarrow\left(x+4\right)\left(x-4\right)=9\Rightarrow x^2-4x+4x-16=9\Rightarrow x^2=25\Rightarrow x=\pm5\)

c, \(\frac{x+2}{2}=\frac{1}{1-x}\Rightarrow\left(x+2\right)\left(1-x\right)=2\Rightarrow x-x^2+2-2x=2\Rightarrow-x^2-x=0\Rightarrow-x\left(x+1\right)=0\Rightarrow\orbr{\begin{cases}x=0\\x+1=0\end{cases}\Rightarrow\orbr{\begin{cases}x=0\\x=-1\end{cases}}}\)