a, \(\frac{x-1}{x+2}+1=\frac{1}{x-2}\)
ĐKXĐ: x + 2 \(\ne\) 0 và x - 2 \(\ne\) 0
\(\Rightarrow\) x \(\ne\) \(\pm\) 2
b, \(\frac{x-1}{1-2x}=1\)
ĐKXĐ: 1 - 2x \(\ne\) 0
\(\Leftrightarrow\) x \(\ne\) \(\frac{1}{2}\)
Bài 2:
a, \(\frac{x+2}{x}=\frac{2x+3}{x-2}\) (ĐKXĐ: x \(\ne\) 0; x \(\ne\) 2)
\(\Leftrightarrow\) \(\frac{\left(x+2\right)\left(x-2\right)}{x\left(x-2\right)}=\frac{x\left(2x+3\right)}{x\left(x-2\right)}\)
\(\Rightarrow\) (x + 2)(x - 2) = x(2x + 3)
\(\Leftrightarrow\) x2 - 4 = 2x2 + 3x
\(\Leftrightarrow\) x2 - 2x2 - 3x = 4
\(\Leftrightarrow\) -x2 - 3x = 4
\(\Leftrightarrow\) -x2 - 3x - 4 = 0
\(\Leftrightarrow\) -(x2 + 3x + 4) = 0
\(\Leftrightarrow\) x2 + 3x + 4 = 0
\(\Leftrightarrow\) x2 + 3x + \(\frac{9}{4}\) + \(\frac{7}{4}\) = 0
\(\Leftrightarrow\) (x + \(\frac{3}{2}\))2 + \(\frac{7}{4}\) = 0
Vì (x + \(\frac{3}{2}\))2 + \(\frac{7}{4}\) > 0 với mọi x
\(\Rightarrow\) Pt vô nghiệm
Vậy S = \(\varnothing\)
b, \(\frac{2x+5}{2x}-\frac{x}{x+5}=0\) (ĐKXĐ: x \(\ne\) 0; x \(\ne\) -5)
\(\Leftrightarrow\) \(\frac{\left(2x+5\right)\left(x+5\right)}{2x\left(x+5\right)}-\frac{2x^2}{2x\left(x+5\right)}=0\)
\(\Rightarrow\) (2x + 5)(x + 5) - 2x2 = 0
\(\Leftrightarrow\) 2x2 + 10x + 5x + 25 - 2x2 = 0
\(\Leftrightarrow\) 15x + 25 = 0
\(\Leftrightarrow\) x = \(\frac{-5}{3}\) (TMĐKXĐ)
Vậy S = {\(\frac{-5}{3}\)}
c, \(\frac{x+1}{3-x}=2\)
\(\Leftrightarrow\) \(\frac{x+1}{3-x}=\frac{2\left(3-x\right)}{3-x}\) (ĐKXĐ: x \(\ne\) 3)
\(\Rightarrow\) x + 1 = 2(3 - x)
\(\Leftrightarrow\) x + 1 - 2(3 - x) = 0
\(\Leftrightarrow\) x + 1 - 6 + 2x = 0
\(\Leftrightarrow\) 3x - 5 = 0
\(\Leftrightarrow\) x = \(\frac{5}{3}\) (TMĐKXĐ)
Vậy S = {\(\frac{5}{3}\)}
d, \(\frac{x+1}{x-1}-\frac{x-1}{x+1}=\frac{16}{x^2-1}\) (ĐKXĐ: x \(\ne\) \(\pm\) 1)
\(\Leftrightarrow\) \(\frac{\left(x+1\right)^2}{\left(x-1\right)\left(x+1\right)}-\frac{\left(x-1\right)^2}{\left(x-1\right)\left(x+1\right)}=\frac{16}{\left(x-1\right)\left(x+1\right)}\)
\(\Rightarrow\) (x + 1)2 - (x - 1)2 = 16
\(\Leftrightarrow\) (x + 1 - x + 1)(x + 1 + x - 1) = 16
\(\Leftrightarrow\) 4x = 16
\(\Leftrightarrow\) x = 4 (TMĐKXĐ)
Vậy S = {4}
Chúc bn học tốt!!