Question

M = \(\left(\frac{1}{a^2-a}+\frac{1}{a-1}\right):\frac{a+1}{a^2-2a+1}\)

Tìm điều kiện xác định và rút gọn M

Answer 1

\(M=\left(\frac{1}{a^2-a}+\frac{1}{a-1}\right):\frac{a+1}{a^2-2a+1}\)

\(M=\left(\frac{1}{a\left(a-1\right)}+\frac{1}{a-1}\right):\frac{a+1}{\left(a-1\right)^2}\)ĐKXĐ : a khác 0, a khác 1

\(M=\frac{1+a}{a\left(a-1\right)}.\frac{\left(a-1\right)^2}{a+1}\)

\(M=\frac{a-1}{a}\)

Answer 2

\(M=\left(\frac{1}{a^2-a}+\frac{1}{a-1}\right):\frac{a+1}{a^2-2a+1}\)DK : \(x\ne0;\pm1\)

\(=\left(\frac{1}{a\left(a-1\right)}+\frac{1}{a-1}\right):\frac{a+1}{\left(a-1\right)^2}=\left(\frac{1}{a\left(a-1\right)}+\frac{a}{a\left(a-1\right)}\right):\frac{a+1}{\left(a-1\right)^2}\)

\(=\frac{a+1}{a\left(a-1\right)}.\frac{\left(a-1\right)^2}{a+1}=\frac{a-1}{a}\)