$B=\dfrac{1}{2\left(\sqrt{x+3}-1\right)}-\dfrac{1}{2\left(\sqrt{x+3}+1\right)}$
$=\dfrac{\sqrt{x+3}+1}{2\left(\sqrt{x+3}-1\right)\left(\sqrt{x+3}+1\right)}-\dfrac{\sqrt{x+3}-1}{2\left(\sqrt{x+3}-1\right)\left(\sqrt{x+3}+1\right)}$
$=\dfrac{\sqrt{x+3}+1-\left(\sqrt{x+3}-1\right)}{2\left(\sqrt{x+3}-1\right)\left(\sqrt{x+3}+1\right)}$
$=\dfrac{2}{2\left(\sqrt{x+3}-1\right)\left(\sqrt{x+3}+1\right)}$
$=\dfrac{2}{2\left(x+2\right)}$
$B=\dfrac{1}{x+2}$ `;(x+2!=0 ⇔ x!=-2)`
