Multiplying by a conjugate to rewrite each of these expressions with the hope that it can written more simply. You can check your answer by testing the initial expression and your result at some simple values of the variables to ensure they’re equal.
\(\displaystyle \frac{9-x}{3-\sqrt{x}} \)
\(\displaystyle \frac{3+\sqrt{x-5}}{x-14} \)
\(\displaystyle \frac{\sqrt{2x+1}-5}{x-2} \)
\(\displaystyle \frac{5}{\sqrt{5y-6}+7} \)
\(\displaystyle \frac{8-u\sqrt{u}}{4-u} \)
\(\displaystyle \frac{\sqrt{t+3}-\sqrt{t}}{3} \)
\(\displaystyle \frac{1}{\sqrt{a}+\sqrt{b}} \)
\(\displaystyle \frac{\sqrt{7+h}-\sqrt{7-h}}{h} \)
\(\displaystyle \frac{t-\sqrt{t^2+5t+10}}{t+2} \)
\(\displaystyle \frac{\sqrt{z+1}}{\sqrt{\sqrt{z+1}+1}+1} \)