813 Вправа 813Алгебра 8 клас Бевз 2025 · § 16 · стор. 154

813. Rationalize a denominator of the fraction.

a) ${\displaystyle \frac{6}{\sqrt{7}-2}=}$${\displaystyle \frac{6\left(\sqrt{7}+2\right)}{7-4}=}$${\displaystyle 2\left(\sqrt{7}+2\right)}$;

b) ${\displaystyle \frac{10}{\sqrt{5}+\sqrt{3}}=}$${\displaystyle \frac{10\left(\sqrt{5}-\sqrt{3}\right)}{5-3}=}$${\displaystyle 5\left(\sqrt{5}-\sqrt{3}\right)}$;

c) ${\displaystyle \frac{22}{2\sqrt{3}+1}=}$${\displaystyle \frac{22\left(2\sqrt{3}-1\right)}{12-1}=}$${\displaystyle 2\left(2\sqrt{3}-1\right)}$;

d) ${\displaystyle \frac{a}{\sqrt{a}-\sqrt{b}}=}$${\displaystyle \frac{a\left(\sqrt{a}+\sqrt{b}\right)}{a-b}}$.