Question

Answer 1

a: \(M=\left(\dfrac{x}{\left(x-5\right)\left(x+5\right)}-\dfrac{x-5}{x\left(x+5\right)}\right)\cdot\dfrac{x\left(x+5\right)}{2x-5}\)

\(=\dfrac{x^2-x^2+10x-25}{x\left(x-5\right)\left(x+5\right)}\cdot\dfrac{x\left(x+5\right)}{2x-5}\)

\(=\dfrac{5\left(2x-5\right)}{2x-5}\cdot\dfrac{1}{x-5}=\dfrac{5}{x-5}\)

b: Thay x=2,5 vào M, ta được:

\(M=\dfrac{5}{2.5-5}=\dfrac{5}{-2.5}=-2\)

c: Để M nguyên thì \(x-5\in\left\{1;-1;5;-5\right\}\)

hay \(x\in\left\{6;4;10\right\}\)