Question

Giai Phương Trình có chứa ẩn ở mẫu:

a)\(\frac{x}{x-1}\) - \(\frac{2x}{x^2-1}\)=0

b)\(\frac{x+2}{x}\)=\(\frac{2x+13}{x\left(x-2\right)}\)

 

 

Answer 1

a, ĐKXĐ: \(x\ne\pm1\)

\(\dfrac{x}{x-1}-\dfrac{2x}{x^2-1}=0\)

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

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

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

\(\Leftrightarrow x\left(x-1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\left(TMĐK\right)\\x=1\left(KTMĐK\right)\end{matrix}\right.\)

Vậy...........

b, ĐKXĐ: \(x\ne0\) ; \(x\ne2\)

\(\Leftrightarrow\dfrac{x^2-4}{x\left(x-2\right)}-\dfrac{2x+13}{x\left(x-2\right)}=0\)

\(\Rightarrow x^2-4-2x-13=0\)

\(\Leftrightarrow x^2-2x-17=0\)

\(\Leftrightarrow\left(x-1\right)^2-16=0\)

\(\Leftrightarrow\left(x-5\right)\left(x+3\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-5=0\\x+3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=5\\x=-3\end{matrix}\right.\left(TMĐK\right)}}\)

Vậy.............

mk làm hơi tắt nha bn

Answer 2

mi học lớp mấy

 

Answer 3

[Math Processing Error]

chỗ này bị lỗi nên mk sua lại

\(\Leftrightarrow\left[{}\begin{matrix}x-5=0\\x+3=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=5\\x=-3\end{matrix}\right.\) (TMĐK)