Question

\(P=\dfrac{x^2-4}{x^2-5x+6}\)

a, rút gọn P

b, tính giá trị của P khi x=- \(\dfrac{2}{3}\)

Answer 1

a) \(P=\dfrac{x^2-4}{x^2-5x+6}=\dfrac{\left(x+2\right)\left(x-2\right)}{\left(x-2\right)\left(x-3\right)}=\dfrac{x+2}{x-3}\left(x\ne2,x\ne3\right)\) (*)

b) thay x=\(-\dfrac{2}{3}\) vào (*) ta được:

P'=\(\dfrac{-\dfrac{2}{3}+2}{-\dfrac{2}{3}-3}=-\dfrac{4}{11}\)

Answer 2

a) \(P=\dfrac{x^2-4}{x^2-5x+6}\)

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

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

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

b) Thay \(x=\dfrac{-2}{3}\) vào biểu thức \(P=\dfrac{x+2}{x-3}\) ta được:

\(P=\dfrac{\dfrac{-2}{3}+2}{\dfrac{-2}{3}-3}=\dfrac{\dfrac{4}{3}}{\dfrac{-11}{3}}=\dfrac{-4}{11}\)

Answer 3

\(a)P=\dfrac{x^2-4}{x^2-5x+6}\\ P=\dfrac{\left(x-2\right)\left(x+2\right)}{x^2-2x-3x+6}\\ P=\dfrac{\left(x-2\right)\left(x+2\right)}{x\left(x-2\right)-3\left(x-2\right)}\\ P=\dfrac{\left(x-2\right)\left(x+2\right)}{\left(x-2\right)\left(x-3\right)}\\ P=\dfrac{x+2}{x-3}\)

b) Thay \(x=-\dfrac{2}{3}\) vào biểu thức \(P=\dfrac{x+2}{x-3}\), ta được:

\(P=\dfrac{-\dfrac{2}{3}+2}{-\dfrac{2}{3}-3}=\dfrac{\dfrac{4}{3}}{-\dfrac{11}{3}}=-\dfrac{4}{11}\)