Question

chi tiết từng bước với ạ vì mình ko hiểu ạ

Answer 1

ko bt

Answer 2

a: \(Q=\dfrac{2x^2-4x+x-3-6}{\left(x-3\right)\left(x-2\right)}\cdot\dfrac{x-2}{x^2+1}=\dfrac{2x^2-3x-9}{x-3}\cdot\dfrac{1}{x^2+1}\)

\(=\dfrac{2x^2-6x+3x-9}{x-3}\cdot\dfrac{1}{x^2+1}=\dfrac{2x+3}{x^2+1}\)

b: Để Q>0 thì 2x+3>0

hay x>-3/2

Answer 3

Bài 2:

a) Q=(\(\dfrac{2x}{x-3}-\dfrac{1}{2-x}-\dfrac{6}{x^2-5x+6}\)):\(\dfrac{x^2+1}{x-2}\)

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

        =[\(\dfrac{2x}{x-3}+\dfrac{1}{x-2}-\dfrac{6}{x\left(x-2\right)-3\left(x-2\right)}\)]:\(\dfrac{x^2+1}{x-2}\)

        =\(\dfrac{2x\left(x-2\right)+x-3-6}{\left(x-2\right)\left(x-3\right)}\):\(\dfrac{x^2+1}{x-2}\)

        =\(\dfrac{2x^2-4x+x-9}{\left(x-2\right)\left(x-3\right)}\):\(\dfrac{x^2+1}{x-2}\)

        =\(\dfrac{2x^2-3x-9}{\left(x-2\right)\left(x-3\right)}\):\(\dfrac{x^2+1}{x-2}\)

        =\(\dfrac{2x^2-6x+3x-9}{\left(x-2\right)\left(x-3\right)}\):\(\dfrac{x^2+1}{x-2}\)

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

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

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

         =\(\dfrac{2x+3}{x^2+1}\)

Answer 4

Để \(\dfrac{1}{Q}\)=\(\dfrac{x^2+1}{2x+3}\)là số nguyên thì x²+1 chia hết cho 2x+3

x²       +1                 2x+3

x²+\(\dfrac{3}{2}\)x                     \(\dfrac{1}{2}\)x-\(\dfrac{3}{4}\)

______

     -\(\dfrac{3}{2}\)x+1

     -\(\dfrac{3}{2}\)x-\(\dfrac{9}{4}\)

____________

            \(\dfrac{13}{4}\)

=>\(\dfrac{1}{Q}\)không nguyên