\(A=\dfrac{x^3+x^2+x^2-5x-6}{x^2+x-6}\)
\(A=\dfrac{x^2\left(x+1\right)+\left(x-6\right)\left(x+1\right)}{\left(x-2\right)\left(x+3\right)}\)
\(A=\dfrac{\left(x+1\right)\left(x^2+x-6\right)}{\left(x-2\right)\left(x+3\right)}\)
\(A=\dfrac{\left(x+1\right)\left(x-2\right)\left(x+3\right)}{\left(x-2\right)\left(x+2\right)}=x+1\)
b) Đề sai rồi, A nguyên với mọi x nguyên nhé
\(A=\dfrac{x^3+2x^2-5x-6}{x^2+x-6}\); (ĐKXĐ: x ≠ 2; x ≠ -3 )
\(=\dfrac{x^3+3x^2-x^2-3x-2x-6}{x^2-2x+3x-6}\)
\(=\dfrac{x^2\left(x+3\right)-x\left(x+3\right)-2\left(x+3\right)}{x\left(x-2\right)+3\left(x-2\right)}\)
\(=\dfrac{\left(x+3\right)\left(x^2-x-2\right)}{\left(x+3\right)\left(x-2\right)}\)
\(=\dfrac{x^2-x-2}{x-2}\)
\(=\dfrac{x^2+x-2x-2}{x-2}\)
\(=\dfrac{\left(x-2\right)\left(x+1\right)}{x-2}\)
\(=x+1\)
