Question

cho bt: B= 10x/x²+3x-4 - 2x-3/x+4 +x+1/1-x

a) rut gon b

b) chung minh b>-3

c) tim gia tri lon nhat cua b

Answer 1

a: \(B=\dfrac{10x}{\left(x+4\right)\left(x-1\right)}-\dfrac{2x-3}{x+4}-\dfrac{x+1}{x-1}\)

\(=\dfrac{10x-\left(2x^2-2x-3x+3\right)-\left(x^2+5x+4\right)}{\left(x+4\right)\left(x-1\right)}\)

\(=\dfrac{10x-2x^2+5x-3-x^2-5x-4}{\left(x+4\right)\left(x-1\right)}\)

\(=\dfrac{-3x^2+10x-7}{\left(x+4\right)\left(x-1\right)}\)

\(=\dfrac{-\left(3x^2-10x+7\right)}{\left(x-1\right)\left(x+4\right)}=-\dfrac{\left(x-1\right)\left(3x-7\right)}{\left(x-1\right)\left(x+4\right)}\)

\(=\dfrac{-3x+7}{x+4}\)

b: \(B+3=\dfrac{-3x+7+3x+12}{x+4}=\dfrac{19}{x+4}>0\)

=>B>-3