Question

M=(1-4/x+1 ) . ]1+2(x^2 +x-4)/9-x^2 ]

a, rút gọn M

b, tìm M khi x=-5

c, tìm x thuộc Z để M thuộc Z  mik daag cần gấp

 

Answer 1

a: \(=\dfrac{x+1-4}{x+1}\cdot\dfrac{9-x^2+2x^2+2x-8}{-\left(x-3\right)\left(x+3\right)}\)

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

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

b: Khi x=-5 thì \(M=\dfrac{-5-1}{-5+3}=\dfrac{-6}{-2}=3\)

c: Để M nguyên thì -x-1 chia hết cho x+3

=>-x-3+2 chia hết cho x+3

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

=>\(x\in\left\{-2;-4;-5\right\}\)