\(\Leftrightarrow\dfrac{x^2+\left(x-2\right)\left(x+2\right)}{x\left(x-2\right)}-2>0\)
\(\Leftrightarrow\dfrac{2x^2-4-2x\left(x-2\right)}{x\left(x-2\right)}>0\)
\(\Leftrightarrow\dfrac{2x^2-4-2x^2+2x}{x\left(x-2\right)}>0\)
\(\Leftrightarrow\dfrac{2x-4}{x\left(x-2\right)}>0\)
=>2/x>0
hay x>0
Giải phương trình sau:
1) 1+\(\dfrac{2x-5}{x-2}-\dfrac{3x-5}{x-1}=0\)
2)\(\dfrac{x-3}{x-2}+\dfrac{x-2}{x-4}=-1\)
3)\(\dfrac{x+1}{x-2}-\dfrac{x-1}{x+2}=\dfrac{2\left(x^2+2\right)}{x^2-4}\)
\(\text{Cho A=}\dfrac{x-2014}{\left(\dfrac{x-2}{x+1}-\dfrac{x+1}{x-2}\right):\left(\dfrac{x-2}{x+1}+\dfrac{x+1}{x-2}\right)}\)
\(\text{Tìm x để A}\ge0\)
\(\dfrac{x+2}{x-2}\)-\(\dfrac{x-2}{x+2}\)= \(\dfrac{-16}{^{^{ }}x^2-4}\)
Bài 1:
a) Giải PT sau: \(\dfrac{x+1}{x-2}-\dfrac{5}{x+2}=\dfrac{12}{x^2-4}+1\)
b) Giải PT sau: |2x+6|-x=3
Giải bất phương trình
\(\dfrac{x^2+2x+2}{x+1}\ge\dfrac{x^2+4x+5}{x+1}-1\)
bài 1 giải BPT
\(\left(x-5\right)^{2^{ }}-x\left(x-2\right)\le4\)
\(\dfrac{x-3}{4}-\dfrac{x-1}{5}< 2\)
\(3-\dfrac{x-4}{2}>x-3\)
1.
\(\dfrac{2x}{x+1}=\dfrac{x^2-x+4}{\left(x-1\right)\left(x-4\right)}\)
giải bất pt;
a)\(\dfrac{x+3}{2011}+\dfrac{x+1}{2013}\ge\dfrac{x+10}{2004}+\dfrac{x+13}{2001}\)
b) (x-5)(x-9)>0
c)\(\dfrac{x-5}{x-8}>2\)
Giải các bất phương trình :
a) \(\dfrac{x^3-4\cdot x^2+5\cdot x-20}{x^3-x^2-10\cdot x-8}>0\)
b) \(\dfrac{x^2+2\cdot x+2}{x+1}>\dfrac{x^2+4\cdot x+5}{x+2}-1\)
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