Question

(1 + x)/(1 - x) + 3 = (x - 3)/(x - 1)
mọi người giúp mình câu này với ạ 

Answer 1

\(\dfrac{1+x}{1-x}+3=\dfrac{x-3}{x-1}\)

\(ĐK:x\ne1\)

\(\Leftrightarrow\dfrac{1+x}{1-x}+3=\dfrac{3-x}{1-x}\)

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

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

\(\Leftrightarrow1+x+3-3x=3-x\)

\(\Leftrightarrow-x=-1\)

\(\Leftrightarrow x=1\left(ktm\right)\)

Vậy pt vô nghiệm

Answer 2

\(\dfrac{1+x}{1-x}+3=\dfrac{x-3}{x-1}\) đề như thế này phải ko?

Answer 3

\(\dfrac{1+x}{1-x}+3=\dfrac{x-3}{x-1}\)

\(ĐK:x\ne1\)

\(\Leftrightarrow\dfrac{1+x}{1-x}+3=\dfrac{3-x}{1-x}\)

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

\(\Leftrightarrow1+x+3\left(1-x\right)=3-x\)

\(\Leftrightarrow1+x+3-3x=3-x\)

\(\Leftrightarrow x=2\)

Vậy \(S=\left\{2\right\}\)