Question

Answer 1

Câu 11:

a: \(P=\left(\dfrac{7}{x^2+x-6}-\dfrac{2}{x-2}\right):\dfrac{1-2x}{x^2-4x+4}\)

\(=\left(\dfrac{7}{\left(x+3\right)\cdot\left(x-2\right)}-\dfrac{2}{x-2}\right):\dfrac{-2x+1}{\left(x-2\right)^2}\)

\(=\dfrac{7-2\left(x+3\right)}{\left(x-2\right)\left(x+3\right)}\cdot\dfrac{\left(x-2\right)^2}{-2x+1}\)

\(=\dfrac{-2x+1}{-2x+1}\cdot\dfrac{x-2}{x+3}=\dfrac{x-2}{x+3}\)

b: Để P nguyên thì \(x-2⋮x+3\)

=>\(x+3-5⋮x+3\)

=>\(-5⋮x+3\)

=>\(x+3\in\left\{1;-1;5;-5\right\}\)

=>\(x\in\left\{-2;-4;2;-8\right\}\)