a) \(P=\left[\frac{2}{3a}-\frac{2}{a+1}\cdot\left(\frac{a+1}{3a}-a-1\right)\right]:\frac{a-1}{a}\)
\(P=\left[\frac{2}{3a}-\frac{2}{a+1}\cdot\left(\frac{a+1-3a^2-3a}{3a}\right)\right]\cdot\frac{a}{a-1}\)
\(P=\left[\frac{2}{3a}-\frac{2}{a+1}\cdot\frac{-3a^2-2a+1}{3a}\right]\cdot\frac{a}{a-1}\)
\(P=\left[\frac{2}{3a}-\frac{2}{a+1}\cdot\frac{\left(a+1\right)\left(-3a+1\right)}{3a}\right]\cdot\frac{a}{a-1}\)
\(P=\left[\frac{2-2\left(-3a+1\right)}{3a}\right]\cdot\frac{a}{a-1}\)
\(P=\frac{6a}{3a}\cdot\frac{a}{a-1}=\frac{2a}{a-1}\)
Vậy...
b) \(2a⋮\left(a-1\right)\)
\(\Leftrightarrow2\left(a-1\right)+2⋮\left(a-1\right)\)
Do đó \(2⋮\left(a-1\right)\)
\(\Rightarrow\left(a-1\right)\inƯ\left(2\right)=\left\{\pm1;\pm2\right\}\)
\(\Leftrightarrow a\in\left\{2;0;3;-1\right\}\)
Mà \(a\ne0;1\) \(\Rightarrow a\in\left\{-1;2;3\right\}\)
Vậy...
c) \(\frac{2a}{a-1}\le1\)
\(\Leftrightarrow\frac{2a}{a-1}-1\le0\)
\(\Leftrightarrow\frac{2a-a+1}{a-1}\le0\)
\(\Leftrightarrow\frac{a+1}{a-1}\le0\)
\(\Leftrightarrow\left(a+1\right)\left(a-1\right)\le0\)
\(\Leftrightarrow-1\le a\le1\)
Vậy....
