\(\dfrac{x^2+3\text{x}y+2y^2}{\left(x^3+2\text{x}^2y\right)-\left(xy^2+2y^3\right)}\)
=\(\dfrac{x^2+3\text{x}y+2y^2}{x^2\left(x+2y\right)-y^2\left(x+2y\right)}\)=\(\dfrac{x^2+3\text{x}y+2y^2}{\left(x+2y\right)\left(x^2-y^2\right)}\)
câu 17
13 a.\(x\)2\(-x\)\(=x(x-1)\)
b.\(2x\)2\(y-6xy\)\(=2xy(x-3) \)
c.\(x\)2\(-3x+2\)=\(x\)2\(-4-3x+6\)
=\((x\)2\(-4)\)\(-(3x-6)\)
=\((x-2)(x+2)-3(x-2)\)
14 a. \(2x(x+2)-3(x+2)=0\)
\(\Rightarrow\)\((x+2)(2x-3)=0\)
\(\Rightarrow\)\(x+2=0\) \(hoặc \) \(2x-3=0\)
\(\Rightarrow\) \(x=-2\) \(hoặc\) \(x=\)\(\dfrac{3}{2}\)
15 a. \(\dfrac{3}{2x+3}-\dfrac{x-3}{2x^2+3x}=\dfrac{3}{2x+3}-\dfrac{x-3}{x\left(2x+3\right)}\)
\(=\dfrac{3.x-\left(x-3\right)}{x\left(2x+3\right)}=\dfrac{3x-x+3}{x\left(2x+3\right)}=\dfrac{2x+3}{x\left(2x+3\right)}=\dfrac{1}{x}\)
b. \(\dfrac{4x-24}{5x-5}\div\dfrac{x^2-36}{x^2-2x+1}=\dfrac{4\left(x-6\right)}{5\left(x-1\right)}\div\dfrac{\left(x-6\right)\left(x+6\right)}{\left(x-1\right)^2}=\dfrac{4\left(x-6\right)}{5\left(x-1\right)}\times\dfrac{\left(x-1\right)^2}{\left(x-6\right)\left(x+6\right)}=\dfrac{4\left(x-1\right)}{5\left(x+6\right)}\)