a/ ĐKXĐ: x khác 1; x khác - 2
pt <=> \(\dfrac{x-1}{\left(x+2\right)\left(x-1\right)}-\dfrac{2\left(x+2\right)}{\left(x+2\right)\left(x-1\right)}=\dfrac{4x-8}{\left(x+2\right)\left(x-1\right)}\)
\(\Leftrightarrow x-1-2x-4=4x-8\Leftrightarrow-5x=-3\Leftrightarrow x=\dfrac{3}{5}\left(tm\right)\)
Vậy........
b/ \(2x-3\ge5\Leftrightarrow2x\ge8\Leftrightarrow x\ge4\)
Vậy......
c,d tt
a. \(\dfrac{1}{x+2}-\dfrac{2}{x-1}=\dfrac{4x-8}{\left(x+2\right)\left(x-1\right)}\)
ĐKXĐ: \(x\ne-2;x\ne1\)
\(\Leftrightarrow\dfrac{1\left(x-1\right)}{x+2\left(x-1\right)}-\dfrac{2\left(x+2\right)}{x-1\left(x+2\right)}=\dfrac{4x-8}{\left(x+2\right)\left(x-1\right)}\)
\(\Rightarrow1\left(x-1\right)-2\left(x+2\right)=4x-8\)
\(\Leftrightarrow x-1-2x-4=4x-8\)
\(\Leftrightarrow x-2x-4x=-8+1+4\)
\(\Leftrightarrow-5x=-3\)
\(\Leftrightarrow x=\dfrac{3}{5}\)
Vậy \(S=\left\{\dfrac{3}{5}\right\}\)
b) \(2x-3\ge5\left(2\right)\)
\(\Leftrightarrow2x\ge8\)
\(\Leftrightarrow x\ge4\)
Vậy tập nghiệm của BPT (2) là \(x\ge4\)
c) \(\dfrac{2}{x+1}-\dfrac{1}{x-2}=\dfrac{2x-6}{\left(x+1\right)\left(x-2\right)}\)
ĐKXĐ: \(x\ne2;x\ne-1\)
\(\Leftrightarrow\dfrac{2\left(x-2\right)}{x+1\left(x-2\right)}-\dfrac{1\left(x+1\right)}{x-2\left(x+1\right)}=\dfrac{2x-6}{\left(x+1\right)\left(x-2\right)}\)
\(\Rightarrow2x-3-1-x=2x-6\)
\(\Leftrightarrow2x-x-2x=-6+3+1\)
\(\Leftrightarrow x=2\) (KTM)
Vậy pt vô \(n_o\)
d) \(3x-5\ge7\left(4\right)\)
\(\Leftrightarrow3x\ge12\)
\(\Leftrightarrow x\ge4\)
Vậy tập nghiệm của BPT (4) là \(x\ge4\)
