bài 4:
a: ĐKXĐ: \(x\notin\left\{2;-2\right\}\)
\(\dfrac{x^2+4x+4}{x^2-4}+\dfrac{x}{2-x}+\dfrac{4-x}{5x-10}\)
\(=\dfrac{\left(x+2\right)^2}{\left(x-2\right)\left(x+2\right)}-\dfrac{x}{x-2}+\dfrac{4-x}{5\left(x-2\right)}\)
\(=\dfrac{x+2}{x-2}-\dfrac{x}{x-2}+\dfrac{4-x}{5\left(x-2\right)}\)
\(=\dfrac{2}{x-2}+\dfrac{4-x}{5\left(x-2\right)}=\dfrac{10+4-x}{5\left(x-2\right)}=\dfrac{14-x}{5\left(x-2\right)}\)
b:ĐKXĐ: \(x\notin\left\{-6;-4\right\}\)
\(\dfrac{x}{x^2+1}-\left(\dfrac{3}{x+6}+\dfrac{2-x}{x+4}\right)+\left[\dfrac{3}{x+6}-\left(\dfrac{1}{x^2+1}-\dfrac{x-2}{x+4}\right)\right]\)
\(=\dfrac{x}{x^2+1}-\dfrac{3}{x+6}-\dfrac{2-x}{x+4}+\dfrac{3}{x+6}-\dfrac{1}{x^2+1}+\dfrac{x-2}{x+4}\)
\(=\dfrac{x}{x^2+1}-\dfrac{1}{x^2+1}+\dfrac{x-2}{x+4}+\dfrac{x-2}{x+4}\)
\(=\dfrac{x-1}{x^2+1}+\dfrac{2x-4}{x+4}\)
\(=\dfrac{\left(x-1\right)\left(x+4\right)+\left(2x-4\right)\left(x^2+1\right)}{\left(x^2+1\right)\left(x+4\right)}\)
\(=\dfrac{x^2+3x-4+2x^3+2x-4x^2-4}{\left(x^2+1\right)\left(x+4\right)}\)
\(=\dfrac{2x^3-3x^2+5x-8}{\left(x^2+1\right)\left(x+4\right)}\)
Bài 3:
a: ĐKXĐ: \(x\notin\left\{0;-1;-2;1\right\}\)
\(\dfrac{1}{x}+\dfrac{2}{x+1}+\dfrac{3}{x+2}-\dfrac{1}{x}-\dfrac{2}{x-1}-\dfrac{3}{x+2}\)
\(=\left(\dfrac{1}{x}-\dfrac{1}{x}\right)+\left(\dfrac{3}{x+2}-\dfrac{3}{x+2}\right)+\dfrac{2}{x+1}-\dfrac{2}{x-1}\)
\(=\dfrac{2}{x+1}-\dfrac{2}{x-1}=\dfrac{2x-2-2x-2}{\left(x+1\right)\left(x-1\right)}=\dfrac{-4}{x^2-1}\)
b: ĐKXĐ: \(x\notin\left\{0;-\dfrac{1}{2};3;-3\right\}\)
\(\dfrac{2x-1}{x}+\dfrac{1-x}{2x+1}+\dfrac{3}{x^2-9}+\dfrac{1-2x}{x}+\dfrac{x-1}{2x+1}-\dfrac{3}{x+3}\)
\(=\left(\dfrac{2x-1}{x}+\dfrac{1-2x}{x}\right)+\left(\dfrac{1-x}{2x+1}+\dfrac{x-1}{2x+1}\right)+\dfrac{3}{\left(x-3\right)\left(x+3\right)}-\dfrac{3}{x+3}\)
\(=\dfrac{3}{\left(x-3\right)\left(x+3\right)}-\dfrac{3}{x+3}\)
\(=\dfrac{3-3\left(x-3\right)}{\left(x+3\right)\left(x-3\right)}=\dfrac{3-3x+9}{\left(x+3\right)\left(x-3\right)}=\dfrac{-3x+12}{\left(x-3\right)\left(x+3\right)}\)
