a: ĐKXĐ: \(x\ne\dfrac{5}{2}\)
\(\dfrac{4x-8}{2x-5}+\dfrac{3-2x}{2x-5}\)
\(=\dfrac{4x-8+3-2x}{2x-5}\)
\(=\dfrac{2x-5}{2x-5}\)
=1
b: ĐKXĐ: \(x\notin\left\{0;3;-3\right\}\)
\(\dfrac{x+9}{x^2-9}-\dfrac{3}{x^2+3x}\)
\(=\dfrac{x+9}{\left(x-3\right)\cdot\left(x+3\right)}-\dfrac{3}{x\left(x+3\right)}\)
\(=\dfrac{x\left(x+9\right)-3\left(x-3\right)}{x\left(x+3\right)\left(x-3\right)}\)
\(=\dfrac{x^2+9x-3x+9}{x\left(x+3\right)\left(x-3\right)}\)
\(=\dfrac{x^2+6x+9}{x\left(x+3\right)\left(x-3\right)}\)
\(=\dfrac{\left(x+3\right)^2}{x\left(x+3\right)\left(x-3\right)}=\dfrac{x+3}{x\left(x-3\right)}\)
c: ĐKXĐ: \(x\notin\left\{-5;6\right\}\)
\(\dfrac{x^2-36}{2x+10}\cdot\dfrac{3}{6-x}\)
\(=\dfrac{\left(x-6\right)\left(x+6\right)}{2\left(x+5\right)}\cdot\dfrac{-3}{x-6}\)
\(=\dfrac{-3\left(x+6\right)}{2\left(x+5\right)}=\dfrac{-3x-18}{2x+10}\)
d: ĐKXĐ: \(x\notin\left\{1;-1;3\right\}\)
\(\dfrac{4x-12}{x^2-1}:\dfrac{x-3}{x+1}\)
\(=\dfrac{4\left(x-3\right)}{\left(x-1\right)\left(x+1\right)}\cdot\dfrac{x+1}{x-3}\)
\(=\dfrac{4}{x-1}\)
\(a,\dfrac{4x-8}{2x-5}+\dfrac{3-2x}{2x-5}\left(x\ne\dfrac{5}{2}\right)\\ =\dfrac{4x-8+3-2x}{2x-5}=\dfrac{2x-5}{2x-5}=1\\ b,\dfrac{x+9}{x^2-9}-\dfrac{3}{x^2+3x}\left(x\ne\pm3;x\ne0\right)\\ =\dfrac{x+9}{\left(x-3\right)\left(x+3\right)}-\dfrac{3}{x\left(x+3\right)}\\ =\dfrac{x\left(x+9\right)-3\left(x-3\right)}{x\left(x+3\right)\left(x-3\right)}\\ =\dfrac{x^2+9x-3x+9}{x\left(x+3\right)\left(x-3\right)}\\ =\dfrac{x^2+6x+9}{x\left(x+3\right)\left(x-3\right)}\\ =\dfrac{\left(x+3\right)^2}{x\left(x+3\right)\left(x-3\right)}\\ =\dfrac{x+3}{x\left(x-3\right)}\)
