Question

a)rút gọn biểu thức

P=x^2/5x+25 + 2x-10/x + 50+5x/x^2+5x

b)Tìm x để P nhận giá trị âm

Answer 1

a)\(P=\dfrac{x^2}{5x+25}+\dfrac{2x-10}{x}+\dfrac{50+5x}{x^2+5x}\left(đkxđ:x\ne0;-5\right)\)

\(P=\dfrac{x^2}{5\left(x+5\right)}+\dfrac{2\left(x-5\right)}{x}+\dfrac{50+5x}{x\left(x+5\right)}\)

\(P=\dfrac{x^3+10\left(x+5\right)\left(x-5\right)+5\left(50+5x\right)}{5x\left(x+5\right)}\)

\(P=\dfrac{x^3+10x^2-250+250+25x}{5x\left(x+5\right)}\)

\(P=\dfrac{x\left(x+5\right)^2}{5x\left(x+5\right)}\)

\(P=\dfrac{x+5}{5}\)

b)P âm\(\Leftrightarrow x+5< 0\Leftrightarrow x< -5\)