giải bất phương trình:
a)\(\frac{2x+1}{x-1}-2\le0\)
b)\(\frac{\left(x-2\right)\left(2x+3\right)}{1-x}\le0\)
c)\(\frac{2}{x-1}\le\frac{5}{2x-1}\)
e)\(\frac{1}{x}+\frac{2}{x+4}< \frac{3}{x+3}\)
f)\(\frac{x+2}{3x+1}\le\frac{x-2}{2x-1}\)
1. Giải các bất phương trình sau :
a, \(\left|3x-7\right|\ge-2x+28\)
b, \(\left|x^2+x-3\right|>x^2+3x+3\)
c, \(\left|x-1\right|+\left|-2x+6\right|\ge x-5\)
d, \(\frac{\left|x-2\right|+7}{\left|4-x\right|+x+1}< 2\)
e, \(\frac{\left|2x-1\right|}{\left(x+1\right)\left(x-2\right)}\le\frac{1}{2}\)
f, \(\frac{\left(2x-3\right)\left(\left|x-1\right|+2\right)}{\left|x-1\right|-2}\le0\)
Giải các bất phương trình sau:
a) \(\frac{x^2-9x+14}{x^2+9x+14}\ge0\)
b) \(\frac{x^2+1}{x^2+3x-10}< 0\)
c) \(\frac{10-x}{5+x^2}>\frac{1}{2}\)
d) \(\frac{x+1}{x-1}+2>\frac{x-1}{x}\)
e) \(\frac{1}{x+1}+\frac{2}{x+3}\le\frac{3}{x+2}\)
f) \(\frac{x-3}{x+1}-\frac{x-2}{x-1}\le\frac{x^2+4x+15}{x^2-1}\)
g) \(\frac{x^2-4x+3}{x^2-2x}\ge0\)
h) \(\frac{x+2}{3x+1}\le\frac{x-2}{2x-1}\)
i) \(\frac{11x^2-5x+6}{x^2+5x+6}\le x\)
j) \(\frac{\left(1-2x\right)\left(\sqrt{3}x+1\right)}{2\sqrt{2}x-1}\ge0\)
k) \(\frac{\left(5x+1\right)-\left(7x-2\right)}{\left(-x^2-1\right)\left(x^2-4x+4\right)}\le0\)
l) \(\frac{1}{x^2-7x+5}\ge\frac{1}{x^2+2x+5}\)
m) \(\frac{\left(x-1\right)\left(x^3-1\right)}{x^2+\left(1+2\sqrt{2}\right)x+2+\sqrt{2}}\le0\)
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Giải các bất phương trình sau
a \(\frac{x^3-2x^2+4x}{-x^2+x+12}>0\)
b \(\frac{4x-3}{x-2}>7-\frac{3x-4}{x+3}\)
c \(\frac{\left(3-x\right)\left(x^2-4x+4\right)}{x^3-x}\le0\)
d \(\frac{2x-3}{3x+5}< \frac{3x+5}{2x-3}\)
e \(\frac{3x+2}{\left(x+1\right)\left(x+2\right)}\ge1\)
f \(\frac{x^3-3}{x^2-1}\ge3\)
giải bất phương trình
a/\(\frac{x^4-x^2}{x^2+5x+6}\le0\)
b/\(\frac{4x^2+3x-1}{x^2+5x+7}>0\)
c/\(\frac{x^4+x^2+1}{x^2-4x-5}\le0\)
d/\(\frac{-2x^2+7x+7}{x^2-3x-10}\le-1\)
e/\(\frac{2\left(x-4\right)}{\left(x-1\right)\left(x-7\right)}\ge\frac{1}{x-2}\)
Giải bất phương trình
a) \(\left(2x^2+1\right)+4x>2x\left(x-2\right)\)
b)\(\left(4x+3\right)\left(x-1\right)< 6x^2-x+1\)
c)\(\left(\frac{3x}{2}-1\right)^2-\frac{x}{2}\left(\frac{5x}{2}-2\right)\le0\)
d) \(\left(2x+1\right)\left(x-3\right)\left(1-5x\right)< 0\)
e)\(2x^2< 16\)
f) \(x^4>8x\)
\(a,\left(2x^2+1\right)+4x>2x\left(x-2\right)\)
\(\Leftrightarrow2x^2+1+4x>2x^2-4x\)
\(\Leftrightarrow4x+4x>-1\)
\(\Leftrightarrow8x>-1\)
\(\Leftrightarrow x>-\frac{1}{8}\)
\(b,\left(4x+3\right)\left(x-1\right)< 6x^2-x+1\)
\(\Leftrightarrow4x^2-4x+3x-3< 6x^2-x+1\)
\(\Leftrightarrow4x^2-x-3< 6x^2-x+1\)
\(\Leftrightarrow4x^2-6x^2< 1+3\)
\(\Leftrightarrow-2x^2< 4\)
\(\Leftrightarrow x^2>2\)
\(\Leftrightarrow x>\pm\sqrt{2}\)
bài 1: giải hệ bất phương trình sau:
a) \(\left\{{}\begin{matrix}2-x>0\\2x+1>x-2\end{matrix}\right.\)
b) \(\left\{{}\begin{matrix}3\left(x-6\right)< -3\\\frac{5x+1}{2}>7\end{matrix}\right.\)
c) \(\left\{{}\begin{matrix}\frac{x-2}{x-1}\le0\\\left(x-1\right)\left(x+1\right)\le0\end{matrix}\right.\)
bài 2: xét dấu các nhị thức sau:
a) q(x)=\(\frac{\left(x-1\right)\left(2x-7\right)}{\left(2+x\right)^2}\)
b) n(x)=\(\frac{\left(1-2x\right)\left(2x-1\right)}{3+x}\)
bài 3: giải các bất phương trình sau;
a) 2\(\left|x-3\right|-\left|3x+1\right|\le x+5\)
b) \(\left|\frac{3x+1}{x-3}\right|< 3\)
giải các bất phương trình sau:
a) \(\frac{\left(x-2\right)\left(9-x\right)}{x-1}\le0\)
b) \(\frac{x\left(x^2-3x+2\right)}{x+4}\ge0\)
c) \(\frac{x-3}{x+1}>\frac{x+5}{x-2}\)
d) \(\frac{x+1}{x-1}+2>\frac{x-1}{x}\)
e) \(\frac{x-3}{x+5}< \frac{1-2x}{x-3}\)
Giải bất phương trình
a, \(5+\frac{x+4}{5}< x=\frac{x-2}{2}+\frac{x+3}{3}\)
b, \(x+1-\frac{x-1}{3}< \frac{2x+3}{3}\frac{x}{3}+5\)
c, \(\frac{\left(x-3\right)^2}{3}-\frac{\left(2x-1\right)^2}{12}\le x\left(x+1\right)\)
d, \(\frac{2x-3}{4}-\frac{x+1}{3}\ge\frac{1}{2}-\frac{3-x}{5}\)
1. giải các hệ bất phương trình sau
a. \(\left\{{}\begin{matrix}\frac{2x+3}{x-1}\ge1\\\frac{\left(x+2\right)\left(2x-4\right)}{x-1}\le0\end{matrix}\right.\)