261 Вправа 261Алгебра 8 клас Бевз 2025 · § 6 · стор. 57

261. Спрости вираз.

а) ${\displaystyle \frac{m-n}{m}:\frac{m-n}{n}=}$${\displaystyle \frac{m-n}{m}\cdot \frac{n}{m-n}=}$${\displaystyle \frac{n\cancel{\left(m-n\right)}}{m\cancel{\left(m-n\right)}}=}$${\displaystyle \frac{n}{m}}$;

б) ${\displaystyle \frac{m^2-n^2}{a}:\frac{m+n}{a}=}$${\displaystyle \frac{m^2-n^2}{a}\cdot \frac{a}{m+n}=}$${\displaystyle \frac{(m^2-n^2)\cdot a}{a\cdot (m+n)}}$=

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

в) ${\displaystyle \frac{1}{m+n}:(m+n)=}$${\displaystyle \frac{1}{m+n}\cdot \frac{1}{m+n}}$=

=${\displaystyle \frac{1}{(m+n)\cdot (m+n)}=}$${\displaystyle \frac{1}{{\left(m+n\right)}^2}}$.