156 Вправа 156Алгебра 8 клас Бевз 2025 · § 4 · стор. 36

156. Спрости вираз.

а) ${\displaystyle \frac{2}{m^2-4}+\frac{m}{m^2-4}=}$${\displaystyle \frac{2}{(m-2)(m+2)}+\frac{m}{(m-2)(m+2)}}$=

=${\displaystyle \frac{\cancel{\left(m+2\right)}}{(m-2)\cancel{\left(m+2\right)}}=}$${\displaystyle \frac{1}{m-2}}$;

б) ${\displaystyle \frac{5a-1}{a^2-b^2}-\frac{5b-1}{a^2-b^2}=}$${\displaystyle \frac{5a-1}{(a-b)(a+b)}-\frac{5b-1}{(a-b)(a+b)}}$=

=${\displaystyle \frac{5a-1-(5b-1)}{(a-b)(a+b)}=}$${\displaystyle \frac{5a-1-5b+1}{(a-b)(a+b)}=}$${\displaystyle \frac{5a-5b}{(a-b)(a+b)}}$=

=${\displaystyle \frac{5\cancel{\left(a-b\right)}}{(a+b)\cancel{\left(a-b\right)}}=}$${\displaystyle \frac{5}{a+b}}$;

в) ${\displaystyle \frac{a^2-30}{a-5}+\frac{5}{a-5}=}$${\displaystyle \frac{a^2-30+5}{a-5}=}$${\displaystyle \frac{a^2-25}{a-5}}$=

=${\displaystyle \frac{(a+5)\cancel{\left(a-5\right)}}{\cancel{\left(a-5\right)}}=}$${\displaystyle a+5}$.