a.
\(A=\dfrac{5}{\left(-\dfrac{1}{2}-1\right)^2}=\dfrac{20}{9}\)
b.
\(P=\dfrac{5}{x^2-2x+1}:\left(\dfrac{x}{x-1}-\dfrac{x+1}{x}\right)\)
\(=\dfrac{5}{\left(x-1\right)^2}:\left(\dfrac{x^2-\left(x-1\right)\left(x+1\right)}{x\left(x-1\right)}\right)\)
\(=\dfrac{5}{\left(x-1\right)^2}:\left(\dfrac{x^2-x^2+1}{x\left(x-1\right)}\right)=\dfrac{5}{\left(x-1\right)^2}.x\left(x-1\right)\)
\(=\dfrac{5x}{x-1}\)
c.
\(P=\dfrac{5x}{x-1}=\dfrac{5x-5+5}{x-1}=5+\dfrac{5}{x-1}\)
Để \(P\in Z\Rightarrow\dfrac{5}{x-1}\in Z\Rightarrow x-1=Ư\left(5\right)\)
\(\Rightarrow x-1=\left\{1;5\right\}\) (do x nguyên dương)
\(\Rightarrow x=\left\{2;7\right\}\)
