Question

Rút gọn biểu thức: 

\(\frac{x^2+x-6}{x^3-4x^2-18x+9}\)

Answer 1

\(\frac{x^2+x-6}{x^3-4x^2-18x+9}=\frac{x^2+3x-2x-6}{x^3+3x^2-7x^2-21x+3x+9}\)

\(=\frac{x\left(x+3\right)-2\left(x+3\right)}{x^2\left(x+3\right)-7x\left(x+3\right)+3\left(x+3\right)}\)

\(=\frac{\left(x+3\right)\left(x-2\right)}{\left(x+3\right)\left(x^2-7x+3\right)}=\frac{x-2}{x^2-7x+3}\) (điều kiện: x khác -3)

Answer 2

t phân tích \(x^2-7x+3\) được như này =)) 

\(x^2-7x+3=x^2-2.x.\frac{7}{2}+\left(\frac{7}{2}\right)^2-\frac{49}{4}+3\)

\(=\left(x-\frac{7}{2}\right)^2-\frac{37}{4}\)

\(=\left(x-\frac{7}{2}\right)^2-\left(\frac{\sqrt{37}}{2}\right)^2\)

\(=\left(x-\frac{7}{2}-\frac{\sqrt{37}}{2}\right)\left(x-\frac{7}{2}+\frac{\sqrt{37}}{2}\right)\)

\(=\left(x-\frac{7+\sqrt{37}}{2}\right)\left(x-\frac{7-\sqrt{37}}{2}\right)\)

Answer 3

\(\frac{x^2+x-6}{x^3-4x^2-18x+9}\)\(=\frac{x^2+3x-2x-6}{x^2+3x^2-7x^2-21x+3x+9}\)

                   \(=\frac{x\left(x+3\right)-2\left(x+3\right)}{\left(x^3+3x^2\right)-\left(7x^2+21x\right)+\left(3x+9\right)}\)

                     \(=\frac{\left(x+3\right)\left(x-2\right)}{x^2\left(x+3\right)-7x\left(x+3\right)+3\left(x+3\right)}\)

                   \(=\frac{\left(x+3\right)\left(x-2\right)}{\left(x+3\right)\left(x^2-7x+3\right)}\)

                  \(=\frac{x-2}{x^2-7x+3}\)

Xong rồi phân tích \(x^2-7x+3\) nữa thì phải =))

Answer 4

\(\frac{x^2+x-6}{x^3-4x^2-18x+9}=\frac{x^2+3x-2x-6}{x^3+3x^2-7x^2-21x+3x+9}\)

\(=\frac{x\left(x+3\right)-2\left(x+3\right)}{x^2\left(x+3\right)-7x\left(x+3\right)+3\left(x+3\right)}=\frac{\left(x-2\right)\left(x+3\right)}{\left(x^2-7x+3\right)\left(x+3\right)}\)

\(=\frac{x-2}{x^2-7x+3}\)

   HỌC TỐT !