a) \(\dfrac{4}{x^2-9}và\dfrac{1-2}{x^2+3x}\)
\(\dfrac{4}{x^2-9}=\dfrac{4}{\left(x-3\right)\left(x+3\right)}\)
\(\dfrac{1-2}{x^2+3x}=\dfrac{1-2}{x\left(x+3\right)}\)
MTC: \(x\left(x-3\right)\left(x+3\right)\)
\(\dfrac{4}{x^2-9}=\dfrac{4}{\left(x-3\right)\left(x+3\right)}=\dfrac{4x}{x\left(x-3\right)\left(x+3\right)}\)
\(\dfrac{1-2}{x^2+3x}=\dfrac{1-2}{x\left(x+3\right)}=\dfrac{1-2}{x\left(x-3\right)\left(x+3\right)}\)
b) \(\dfrac{1}{6x^2y^3};\dfrac{-5}{22x^3y^2}và\dfrac{9}{14x^4y}\)
MTC: \(462x^4y^3\)
\(\dfrac{1}{6x^2y^3}=\dfrac{77x^2}{462x^4y^3}\)
\(\dfrac{-5}{22x^3y^2}=\dfrac{-105xy}{462x^4y^3}\)
\(\dfrac{9}{14x^4y}=\dfrac{297y^2}{462x^4y^3}\)
Bài 1 :
Câu a :\(\dfrac{7x\left(x^2-4\right)}{3x^2+6x}=\dfrac{7x\left(x-2\right)\left(x+2\right)}{3x\left(x+2\right)}=\dfrac{7x\left(x-2\right)}{3x}\)
Câu c : \(\dfrac{x^2-5x+6}{x^2-2x}=\dfrac{\left(x-2\right)\left(x-3\right)}{x\left(x-2\right)}=\dfrac{x-3}{x}\)
Câu b : \(\dfrac{x^3+27}{x+3}=\dfrac{\left(x+3\right)\left(x^2-3x+9\right)}{\left(x+3\right)}=x^2-3x+9\)
Câu d : \(\dfrac{x^2-xy+x-y}{x^2-xy-x+y}=\dfrac{x\left(x-y\right)+\left(x-y\right)}{x\left(x-y\right)-\left(x-y\right)}=\dfrac{\left(x-y\right)\left(x+1\right)}{\left(x-y\right)\left(x-1\right)}=\dfrac{\left(x+1\right)}{\left(x-1\right)}\)
