Question

Cho biểu thức P \(=\frac{x^3-6x^2+11x-12}{x^2-5x+4}\)

a) Rút gọn P

b) Tìm x để P nguyên

Answer 1

P=\(\frac{x^3-6x^2+11x-12}{x^2-5x+4}\)

=\(\frac{x^3-4x^2-2x^2+8x+3x-12}{x^2-x-4x+4}\)

=\(\frac{\left(x-4\right)\left(x^2-2x+3\right)}{\left(x-1\right)\left(x-4\right)}\)

=\(\frac{x^2-2x+3}{x-1}\)

b,

\(\frac{x^2-2x+3}{x-1}\) =\(2x-x^2-\left(\frac{3}{x-1}\right)\) \(\Leftrightarrow\) x-1 \(\in\) (Ư)3

\(\begin{cases}x-1=3\\x-1=-3\end{cases}\) \(\Leftrightarrow\) x₁=4 ,x₂=-2

vậy x={4,-2}