a) ĐKXĐ: \(x\ne\pm5\)
MTC: \(3\left(x+5\right)\left(x-5\right)\)
Ta có:
\(\dfrac{5}{3x+15}=\dfrac{5}{3\left(x+5\right)}=\dfrac{5\left(x-5\right)}{3\left(x+5\right)\left(x-5\right)}=\dfrac{5x-25}{3\left(x+5\right)\left(x-5\right)}\) ;
\(\dfrac{3}{x^2-25}=\dfrac{3}{\left(x+5\right)\left(x-5\right)}=\dfrac{9}{3\left(x+5\right)\left(x-5\right)}\)
b) ĐKXĐ: \(x\ne0;x\ne\pm1\)
MTC: \(x\left(x+1\right)\)
Ta có:
\(\dfrac{x^2-x}{x^2-1}=\dfrac{x\left(x-1\right)}{\left(x-1\right)\left(x+1\right)}=\dfrac{x}{x+1}=\dfrac{x^2}{x\left(x+1\right)}\) ;
\(\dfrac{3x+3}{x^3+2x^2+x}=\dfrac{3\left(x+1\right)}{x\left(x^2+2x+1\right)}=\dfrac{3\left(x+1\right)}{x\left(x+1\right)^2}=\dfrac{3}{x\left(x+1\right)}\) ;
\(\dfrac{2x}{x^2}=\dfrac{2}{x}=\dfrac{2\left(x+1\right)}{x\left(x+1\right)}=\dfrac{2x+2}{x\left(x+1\right)}\)
c) ĐKXĐ: \(x\ne\pm5\)
MTC: \(\left(x-5\right)\left(x+5\right)\)
Ta có:
\(\dfrac{3x^2-4x+1}{x^2-25}=\dfrac{3x^2-4x+1}{\left(x-5\right)\left(x+5\right)}\) ;
\(\dfrac{x-3}{5-x}=\dfrac{3-x}{x-5}=\dfrac{\left(3-x\right)\left(x+5\right)}{\left(x-5\right)\left(x+5\right)}=\dfrac{-x^2-2x+15}{\left(x-5\right)\left(x+5\right)}\) ;
\(\dfrac{4x}{x+5}=\dfrac{4x\left(x-5\right)}{\left(x-5\right)\left(x+5\right)}=\dfrac{4x^2-20x}{\left(x-5\right)\left(x+5\right)}\)
\(\text{#}Toru\)
