Question

giúp mình với ạ

Answer 1

a: ĐKXĐ: \(x\notin\left\{5;-2;2\right\}\)

\(M=\dfrac{2x-10}{x^2-7x+10}-\dfrac{2x}{x^2-4}+\dfrac{1}{2-x}\)

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

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

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

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

b: Để M là số nguyên thì \(-1⋮x+2\)

=>\(x+2\in\left\{1;-1\right\}\)

=>\(x\in\left\{-1;-3\right\}\)