Question

a) Rút gọn A

b) Tìm X thuộc Z để \(\dfrac{A}{2}\)thuộc Z

c) Tìm X để A = \(\dfrac{1}{x-1}\)

A=\(\dfrac{2x-5}{x^2-5x+6}+\dfrac{x+2}{x-3}+\dfrac{3-x}{2-x}\)

Answer 1

a: \(A=\dfrac{2x-5+x^2-4+x^2-9}{\left(x-2\right)\left(x-3\right)}=\dfrac{2x^2+2x-18}{\left(x-2\right)\left(x-3\right)}\)

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

b: Để A/2=x+3/x-3 là số nguyên thì \(x-3+6⋮x-3\)

=>\(x-3\in\left\{1;-1;2;-2;3;-3;6;-6\right\}\)

hay \(x\in\left\{4;51;6;0;9;-3\right\}\)

c: Để A=1/x-1 thì \(\dfrac{2x+6}{x-3}=\dfrac{1}{x-1}\)

=>2x^2-2x+6x-6=x-3

=>2x^2+5x-6-x+3=0

=>2x^2+4x-3=0

hay \(x=\dfrac{-2\pm\sqrt{10}}{2}\)