Đáp án:
Giải thích các bước giải:
a,
ĐKXĐ x khác 0,-5,-2
$P=$[$\dfrac{x^2+9}{x(x+5)}$+ $\dfrac{(x-1)(x+5)}{x(x+5)}$- $\dfrac{x^2}{x(x+5)}$]:$(1+$ $\dfrac{2}{x}$)
=$\dfrac{x^2+9+x^2+4x-5-x^2}{x(x+5)}$: $\dfrac{x+2}{x}$
= $\dfrac{x^2+4x+4}{x(x+5)}$. $\dfrac{x}{x+2}$
= $\dfrac{(x+2)^2}{(x+5)(x+2)}$
= $\dfrac{x+2}{x+5}$
b,
$(x-2)(3x-2)=0$
⇔\(\left[ \begin{array}{l}x=2\\x=2/3\end{array} \right.\)
Khi $x=2$ ⇒ $P=$$\dfrac{2+2}{2+5}$$=$$\dfrac{4}{7}$
Khi $x=2/3$⇒$P=$$\dfrac{2/3+2}{2/3+5}$=$\dfrac{18}{7}$
c,
$P<1$
⇔$\dfrac{x+2}{x+5}$$<1$
⇔$\dfrac{x+2}{x+5}$$-1<0$
⇔$\dfrac{x+2-x-5}{x+5}$$<0$
⇔$\dfrac{-3}{x+5}$$<0$
⇔$x+5>0$
⇔$x>-5$