Bài 1:
a: ĐKXĐ: x<>0
\(\dfrac{x^2-3x+1}{2x^2}+\dfrac{5x-1-x^2}{2x^2}\)
\(=\dfrac{x^2-3x+1+5x-1-x^2}{2x^2}\)
\(=\dfrac{2x}{2x^2}=\dfrac{1}{x}\)
b: ĐKXĐ: \(x\ne\pm y\)
\(\dfrac{y}{x-y}+\dfrac{x}{x+y}=\dfrac{y\left(x+y\right)+x\left(x-y\right)}{\left(x-y\right)\left(x+y\right)}\)
\(=\dfrac{xy+y^2+x^2-xy}{x^2-y^2}=\dfrac{x^2+y^2}{x^2-y^2}\)
c: ĐKXĐ: \(x\notin\left\{0;3\right\}\)
\(\dfrac{x}{2x-6}+\dfrac{9}{2x\left(3-x\right)}\)
\(=\dfrac{x}{2\left(x-3\right)}-\dfrac{9}{2x\left(x-3\right)}\)
\(=\dfrac{x^2-9}{2x\left(x-3\right)}=\dfrac{\left(x-3\right)\left(x+3\right)}{2x\left(x-3\right)}=\dfrac{x+3}{2x}\)
Bài 2:
a: ĐKXĐ: x<>-1
\(\dfrac{5-3x}{x+1}-\dfrac{-2+5x}{x+1}\)
\(=\dfrac{5-3x+2-5x}{x+1}=\dfrac{-8x+7}{x+1}\)
b: ĐKXĐ: \(x\ne\pm y\)
\(\dfrac{x}{x-y}-\dfrac{y}{x+y}\)
\(=\dfrac{x\left(x+y\right)-y\left(x-y\right)}{\left(x-y\right)\left(x+y\right)}\)
\(=\dfrac{x^2+xy-xy+y^2}{x^2-y^2}=\dfrac{x^2+y^2}{x^2-y^2}\)
c: ĐKXĐ: x<>-1
\(\dfrac{3}{x+1}-\dfrac{3x+2}{x^3+1}\)
\(=\dfrac{3}{x+1}-\dfrac{3x+2}{\left(x+1\right)\left(x^2-x+1\right)}\)
\(=\dfrac{3\left(x^2-x+1\right)-3x-2}{\left(x+1\right)\left(x^2-x+1\right)}\)
\(=\dfrac{3x^2-6x+1}{\left(x+1\right)\left(x^2-x+1\right)}\)
