\(\Leftrightarrow\dfrac{1-2x}{x+1}-\dfrac{1}{x+1}=-2x-6+x+2=-x-4\)
\(\Leftrightarrow-2x=\left(-x-4\right)\left(x+1\right)\)
\(\Leftrightarrow\left(x+4\right)\left(x+1\right)=2x\)
\(\Leftrightarrow x^2+5x+4-2x=0\)
\(\Leftrightarrow x^2+3x+4=0\)
\(\text{Δ}=3^2-4\cdot1\cdot4=9-16=-7< 0\)
Do đó: Phương trình vô nghiệm
giải bất phương trinh sau:
\(\dfrac{x+2}{2x-1}\ge\dfrac{1}{x-2}\)
giải Pt sau :
\(\dfrac{1}{x^2-2x+2}+\dfrac{1}{x^2-2x+3}=\dfrac{9}{2\left(x^2-2x+4\right)}\)
giải pt
\(\dfrac{1}{x^2-2x+2}+\dfrac{2}{x^2-2x+3}=\dfrac{6}{x^2-2x+4}\)
Giải phương trình:
\(\dfrac{x^2-4x+1}{x+1}+2\)\(=\dfrac{x^2-5x+1}{2x+1}\)
Rút gọn \(\left[\dfrac{x}{2x-6}-\dfrac{x^2}{x^2-9}+\dfrac{x}{2x-9}.\left(\dfrac{3}{x}-\dfrac{1}{x-3}\right)\right]:\dfrac{x^2-5x-6}{18-2x^2}\)
Thực hiện phép tính
a, \(\dfrac{x+3}{x-2}\) + \(\dfrac{4+x}{2-x}\)
b, \(\dfrac{x+1}{2x+6}\) + \(\dfrac{2x+3}{x^2+3x}\)
c, \(\dfrac{3}{2x+6}\) - \(\dfrac{x-6}{2x^2+6x}\)
d, \(\dfrac{2x+6}{3x^2-x}\) : \(\dfrac{x^2+3x}{1-3x}\)
Giải :
a) \(\dfrac{7}{8x}+\dfrac{5-x}{4x^2-8x}=\dfrac{x-1}{2x^2-4x}+\dfrac{1}{8x-16}\)
b) \(3x.\left|x+1\right|-2x\left|x+2\right|=12\)
Rút gọn \(\left(\dfrac{1+x}{x}+\dfrac{1}{4x^2}\right)\left(\dfrac{1-2x}{1+2x}-\dfrac{1}{1-4x^2}.\dfrac{1-4x+4x^2}{1+2x}\right)-\dfrac{1}{2x}\)
a.\(\dfrac{x+6}{5}-\dfrac{x-2}{3}< 2\)
b. \(\dfrac{x+5}{4}-\dfrac{x^{2^{ }}-3}{6}\ge1-\dfrac{2x^{2^{ }}-1}{12}\)
c. \(x^{2^{ }}-4x+3>0\)
d. \(x^{3^{ }}-2x^{2^{ }}+3x-2\ge0\)
e. \(\left|x+1\right|+\left|x-2\right|=4\)
f. \(\dfrac{5x-1}{10}+\dfrac{2x+3}{6}>\dfrac{x-8}{15}-\dfrac{x-1}{30}\)
h.\(\dfrac{10x+3}{12}< \dfrac{15-8x}{9}\)
