Question

aRút gọn Biểu thức

b, Tìm x c Z để B c Z

B=x+2/x+3 - 5/x^2 +x-6 + 1/2-x

a,Rút gọn P

b Tìm x để P=0,P=1,P>0

P=x+3/x²+5x+6 : (8x²/4x³-8x² - 3x/3x²-12 - 1/x+2)

help me please

Answer 1

Bài 2: 

a: \(P=\dfrac{x+3}{x^2+5x+6}:\left(\dfrac{8x^2}{4x^3-8x^2}-\dfrac{3x}{3x^2-12}-\dfrac{1}{x+2}\right)\)

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

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

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

\(=\dfrac{1}{x+2}\cdot\dfrac{\left(x-2\right)\left(x+2\right)}{2x+8}=\dfrac{x-2}{2x+8}\)

b: Để P=0 thì x-2=0

hay x=2(loại)

Để P=1 thì 2x+8=x-2

hay x=-10(nhận)

Để P>0 thì \(\dfrac{x-2}{2x+8}>0\)

=>x>2 hoặc x<-4