a) \(\dfrac{5x}{x-1}+\left(-\dfrac{5}{x-1}\right)\)
\(=\dfrac{5x-5}{x-1}\)
\(=\dfrac{5\left(x-1\right)}{x-1}\)
\(=5\)
b) \(\dfrac{1}{x-3}+\dfrac{2}{x+3}+\dfrac{9-x}{x^2-9}\)
\(=\dfrac{1}{x-3}+\dfrac{2}{x+3}+\dfrac{9-x}{\left(x-3\right)\left(x+3\right)}\)
\(=\dfrac{x+3+2\left(x-3\right)+9-x}{\left(x-3\right)\left(x+3\right)}\)
\(=\dfrac{x+3+2x-6+9-x}{\left(x-3\right)\left(x+3\right)}\)
\(=\dfrac{2x+6}{\left(x-3\right)\left(x+3\right)}\)
\(=\dfrac{2\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}\)
\(=\dfrac{2}{x-3}\)
c) \(\dfrac{4x+8}{4-x^2}.\left(x^2-2x\right)\)
\(=\dfrac{4\left(x+2\right)}{\left(2-x\right)\left(2+x\right)}.\dfrac{x\left(x-2\right)}{1}\)
\(=-\dfrac{4x\left(x+2\right)\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}\)
\(=-4x\).
a,\(\dfrac{5x}{x-1}+\dfrac{-5}{x-1}=\dfrac{5x-5}{x-1}=\dfrac{5\left(x-1\right)}{x-1}=5\)
b,\(\dfrac{1}{x-3}+\dfrac{2}{x+3}+\dfrac{9-x}{x^2-9}=\dfrac{1}{x-3}+\dfrac{2}{x+3}+\dfrac{9-x}{\left(x+3\right)\left(x-3\right)}\)
=\(\dfrac{x+3+2\left(x-3\right)+9-x}{\left(x+3\right)\left(x-3\right)}=\dfrac{x+3+2x-6+9}{\left(x+3\right)\left(x-3\right)}\)
\(\dfrac{3x+6}{\left(x+3\right)\left(x-3\right)}=\dfrac{3\left(x+2\right)}{\left(x+3\right)\left(x-3\right)}\)
c,\(\left(\dfrac{4x+8}{4-x^2}\right).x^2-2x=\dfrac{4}{2-x}.\dfrac{x^2-2x}{1}=\dfrac{4x^2-8x}{2-x}\)
=\(\dfrac{-4x\left(2-x\right)}{2-x}=-4x\)