Question

Answer 1

a) ĐKXĐ: \(2x\left(x+5\right)\ne0\Leftrightarrow\left\{{}\begin{matrix}x\ne0\\x\ne-5\end{matrix}\right.\)

b) \(P=A+B=\dfrac{x\left(x^2+2x\right)+\left(x-5\right).2\left(x+5\right)+50-5x}{2x\left(x+5\right)}=\dfrac{x^3+4x^2-5x}{2x\left(x+5\right)}=\dfrac{x\left(x-1\right)\left(x+5\right)}{2x\left(x+5\right)}=\dfrac{x-1}{2}\)

c) \(P=\dfrac{x-1}{2}=0\Leftrightarrow x-1=0\Leftrightarrow x=1\left(tm\right)\)

\(P=\dfrac{x-1}{2}=\dfrac{1}{4}\Leftrightarrow4x-4=2\Leftrightarrow x=\dfrac{3}{2}\left(tm\right)\)

d) \(P=\dfrac{x-1}{2}>0\Leftrightarrow x-1>0\Leftrightarrow x>1\)

\(P=\dfrac{x-1}{2}< 0\Leftrightarrow x-1< 0\Leftrightarrow x< 1,x\ne0,x\ne-5\)