$a)$ $\sqrt{(1-\sqrt{5})^{2}}$ $+$ $1$
$=$ $1$$-$$\sqrt{5}$ $+1$
$=$ $2$$-$$\sqrt{5}$
$b)$ $\sqrt{b^{2}-b+\frac{1}{4}}$$-$$(2b-\frac{1}{2})$
$=$$\sqrt{(b-\frac{1}{2})^{2}}$$-$$2b$$+$$\frac{1}{2}$
$=$ $|$b$-$$\frac{1}{2}$$|$$-$$2b$+$\frac{1}{2}$
$=$ b$-$$\frac{1}{2}$$-$$2b$+$\frac{1}{2}$
$=$ $-b$
$c)$ $\sqrt{3+2\sqrt{2}}$$-2$
$=$ $\sqrt{1+2\sqrt{2}+2}$ $-2$
$=$ $($$\sqrt{1}$+$\sqrt{2}$$)^{2}$$-2$
$=$ $1$+$\sqrt{2}$$-2$
$=$ $\sqrt{2}$$-1$
$d)$ $\frac{\sqrt{(a-1)^{2}}}{a-1}$
$=$ $\frac{|a-1|}{a-1}$
$=$ $\frac{1-a}{a-1}$
$=$ $-1$
