Question

\(N=\left(\dfrac{1-a^3}{1-a}-a\right):\dfrac{1-a^2}{1-a+a^3-a^2}\)

a) Rút gọn N

b) a bằng mấy để N < 0

c) Tìm a thuộc Z để N thuộc Z

Answer 1

a: \(N=\left(\dfrac{\left(1-a\right)\left(a^2+a+1\right)}{1-a}-a\right)\cdot\dfrac{a^3-a^2-a+1}{-\left(a^2-1\right)}\)

\(=\left(a^2+1\right)\cdot\dfrac{a^2\left(a-1\right)-\left(a-1\right)}{-\left(a-1\right)\left(a+1\right)}\)

\(=-\left(a^2+1\right)\cdot\dfrac{\left(a-1\right)\left(a^2-1\right)}{\left(a-1\right)\left(a+1\right)}\)

\(=-\left(a^2+1\right)\cdot\left(a-1\right)\)

b: Để N<0 thì \(-\left(a^2+1\right)\left(a-1\right)< 0\)

\(\Leftrightarrow\left(a^2+1\right)\left(a-1\right)>0\)

=>a-1>0

hay a>1