Câu 1:
a) $P =\left(1+\dfrac{1}{x-1}\right):\dfrac{x}{x^2 -1}\qquad (x\ne 0;\, x \ne \pm 1)$
$\to P =\dfrac{x-1 + 1}{x-1}:\dfrac{x}{(x-1)(x+1)}$
$\to P =\dfrac{x}{x-1}\cdot\dfrac{(x-1)(x+1)}{x}$
$\to P = x+1$
b) $P = 4$
$\to x + 1 = 4$
$\to x = 3$
Câu 2:
a) $Q =\left(\dfrac{1}{x+2}-\dfrac{2}{x^2 + 2x}\right)\cdot\left(1+\dfrac{2}{x-2}\right)\qquad (x\ne 0;\, x \ne \pm 2)$
$\to Q =\left[\dfrac{x}{x(x+2)}-\dfrac{2}{x(x + 2)}\right]\cdot\dfrac{x-2 +2}{x-2}$
$\to Q =\dfrac{x-2}{x(x+2)}\cdot\dfrac{x}{x-2}$
$\to Q =\dfrac{1}{x+2}$
b) $x = -\dfrac12$
$\to x + 2 = \dfrac32$
$\to \dfrac{1}{x+2}=\dfrac23$
$\to Q =\dfrac23$
