a) \(\dfrac{2x-6}{x^2-x-6}\)
\(=\dfrac{2\left(x-3\right)}{x^2-3x+2x-6}\)
\(=\dfrac{2\left(x-3\right)}{x\left(x-3\right)+2\left(x-3\right)}\)
\(=\dfrac{2\left(x-3\right)}{\left(x-3\right)\left(x+2\right)}\)
\(=\dfrac{2}{x+2}\)
b) \(\dfrac{6x^2-x-2}{4x^2-1}\)
\(=\dfrac{6x^2+3x-4x-2}{\left(2x\right)^2-1^2}\)
\(=\dfrac{3x\left(2x+1\right)-2\left(2x+1\right)}{\left(2x-1\right)\left(2x+1\right)}\)
\(=\dfrac{\left(2x+1\right)\left(3x-2\right)}{\left(2x-1\right)\left(2x+1\right)}\)
\(=\dfrac{3x-2}{2x-1}\)
\(c,\dfrac{x^3-x^2+3x-3}{x^3+2x^2+3x+6}\)
\(=\dfrac{x^2\left(x-1\right)+3\left(x-1\right)}{x^2\left(x+2\right)+3\left(x+2\right)}\)
\(=\dfrac{\left(x-1\right)\left(x^2+3\right)}{\left(x+2\right)\left(x^2+3\right)}=\dfrac{x-1}{x+2}\)
d,Sửa đề :
\(\dfrac{a^2-b^2+c^2+2ac}{a^2+b^2-c^2+2ab}\)
\(=\dfrac{\left(a^2+2ac+c^2\right)-b^2}{\left(a^2+2ab+b^2\right)-c^2}\)
\(=\dfrac{\left(a+c\right)^2-b^2}{\left(a+b\right)^2-c^2}\)
\(=\dfrac{\left(a-b+c\right)\left(a+b+c\right)}{\left(a+b-c\right)\left(a+b+c\right)}\)
\(=\dfrac{a-b+c}{a+b-c}\)
e,g Đề ko rõ
\(\dfrac{2x-6}{x^2-x-6}=\dfrac{2\left(x-3\right)}{\left(x^2+2x\right)-\left(3x+6\right)}\\ =\dfrac{2\left(x-3\right)}{x\left(x+2\right)-3\left(x+2\right)}\\ =\dfrac{2\left(x-3\right)}{\left(x+2\right)\left(x-3\right)}=\dfrac{2}{x+2}\)
b.
\(\dfrac{6x^2-x-2}{4x^2-1}\\ =\dfrac{\left(6x^2+3x\right)-\left(4x+2\right)}{\left(2x-1\right)\left(2x+1\right)}\\ =\dfrac{3x\left(2x+1\right)-2\left(2x+1\right)}{\left(2x-1\right)\left(2x+1\right)}\\ =\dfrac{3x-2}{2x-1}\)
c.
\(\dfrac{x^3-x^2+3x-3}{x^3+2x^2+3x+6}\\ =\dfrac{x^2\left(x-1\right)+3\left(x-1\right)}{x^2\left(x+2\right)+3\left(x+2\right)}\\ =\dfrac{\left(x-1\right)^2}{\left(x+2\right)^2}\)