636° Вправа 636Алгебра 8 клас Тарасенкова 2025 · § 15 · стор. 190

636. Спростіть вираз:

1) ${\displaystyle \frac{2\sqrt{y}}{y+\sqrt{y}}=}$${\displaystyle \frac{2\cancel{\sqrt{y}}}{\cancel{\sqrt{y}}(\sqrt{y}+1)}=}$${\displaystyle \frac{2}{\sqrt{y}+1}}$;

2) ${\displaystyle \frac{\sqrt{c}}{3c-\sqrt{c}}=}$${\displaystyle \frac{\cancel{\sqrt{c}}}{\cancel{\sqrt{c}}(3\sqrt{c}-1)}=}$${\displaystyle \frac{1}{3\sqrt{c}-1}}$;

3) ${\displaystyle \frac{\sqrt{12m}-\sqrt{12n}}{\sqrt{3m}-\sqrt{3n}}=}$${\displaystyle \frac{2\cancel{\left(\sqrt{3m}-\sqrt{3n}\right)}}{\cancel{\left(\sqrt{3m}-\sqrt{3n}\right)}}=}$${\displaystyle 2}$;

4) ${\displaystyle \frac{\sqrt{mn}+\sqrt{m}}{1+\sqrt{n}}=}$${\displaystyle \frac{\sqrt{m}\cancel{\left(\sqrt{n}+1\right)}}{\cancel{\left(1+\sqrt{n}\right)}}=}$${\displaystyle \sqrt{m}}$;

5) ${\displaystyle \frac{\sqrt{mp}+\sqrt{2p}}{\sqrt{ma}+\sqrt{2a}}=}$${\displaystyle \frac{\sqrt{p}\cancel{\left(\sqrt{m}+\sqrt{2}\right)}}{\sqrt{a}\cancel{\left(\sqrt{m}+\sqrt{2}\right)}}=}$${\displaystyle \frac{\sqrt{p}}{\sqrt{a}}}$;

6) ${\displaystyle \frac{y-25}{\sqrt{y}+5}=}$${\displaystyle \frac{(\sqrt{y}-5)\cancel{\left(\sqrt{y}+5\right)}}{\cancel{\left(\sqrt{y}+5\right)}}=}$${\displaystyle \sqrt{y}-5}$;

7) ${\displaystyle \frac{n^2-7}{n-\sqrt{7}}=}$${\displaystyle \frac{\cancel{\left(n-\sqrt{7}\right)}(n+\sqrt{7})}{\cancel{\left(n-\sqrt{7}\right)}}=}$${\displaystyle n+\sqrt{7}}$;

8) ${\displaystyle \frac{x-19}{\sqrt{x}+\sqrt{19}}=}$${\displaystyle \frac{(\sqrt{x}-\sqrt{19})\cancel{\left(\sqrt{x}+\sqrt{19}\right)}}{\cancel{\left(\sqrt{x}+\sqrt{19}\right)}}=}$${\displaystyle \sqrt{x}-\sqrt{19}}$.