Question

p=\(\left(\dfrac{x+2}{x^2-5x+6}-\dfrac{x+3}{2-x}-\dfrac{x+2}{x-3}\right):\left(2x+5+\dfrac{9}{x-3}\right)\)
a,rút gọn
b,tìm x ∈ z để p ∈ z

Answer 1

a: \(P=\left(\dfrac{x+2}{\left(x-2\right)\left(x-3\right)}+\dfrac{x+3}{x-2}-\dfrac{x+2}{x-3}\right):\dfrac{\left(2x+5\right)\left(x-3\right)+9}{x-3}\)

\(=\dfrac{x+2+\left(x+3\right)\left(x-3\right)-\left(x+2\right)\left(x-2\right)}{\left(x-2\right)\left(x-3\right)}\cdot\dfrac{x-3}{2x^2-6x+5x-15+9}\)

\(=\dfrac{x+2+x^2-9-x^2+4}{\left(x-2\right)}\cdot\dfrac{1}{2x^2-x-6}\)

\(=\dfrac{x-3}{x-2}\cdot\dfrac{1}{2x^2-4x+3x-6}\)

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

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