38. Сократите дробь: 1) (3m − 3n)/(7m − 7n); 2) (5a + 25b)/(2a² + 10ab); 3) (4x − 16y)/(16y); 4) (x² − 49)/(6x + 42); 5) (12a² − 6a)/(3 − 6a); 6) (9b² − 1)/(9b² + 6b + 1); 7) (b⁵ − b⁴)/(b⁵ − b⁶); 8) (7m² + 7m + 7)/(m³ − 1); 9) (64 − x²)/(3x² − 24x).

Question

Вопрос:

Фото задания: 38. Сократите дробь: 1) (3m − 3n)/(7m − 7n); 2) (5a + 25b)/(2a² + 10ab); 3) (4x − 16y)/(16y); 4) (x² − 49)/(6x + 42); 5)…

38. Сократите дробь: 1) (3m − 3n)/(7m − 7n); 2) (5a + 25b)/(2a² + 10ab); 3) (4x − 16y)/(16y); 4) (x² − 49)/(6x + 42); 5) (12a² − 6a)/(3 − 6a); 6) (9b² − 1)/(9b² + 6b + 1); 7) (b⁵ − b⁴)/(b⁵ − b⁶); 8) (7m² + 7m + 7)/(m³ − 1); 9) (64 − x²)/(3x² − 24x).

Accepted Answer

\(\dfrac{3m-3n}{7m-7n}=\dfrac{3(m-n)}{7(m-n)}=\dfrac37\).
\(\dfrac{5a+25b}{2a^2+10ab}=\dfrac{5(a+5b)}{2a(a+5b)}=\dfrac{5}{2a}\).
\(\dfrac{4x-16y}{16y}=\dfrac{4(x-4y)}{16y}=\dfrac{x-4y}{4y}\).
\(\dfrac{x^2-49}{6x+42}=\dfrac{(x-7)(x+7)}{6(x+7)}=\dfrac{x-7}{6}\).
\(\dfrac{12a^2-6a}{3-6a}=\dfrac{6a(2a-1)}{3(1-2a)}=-2a\).
\(\dfrac{9b^2-1}{9b^2+6b+1}=\dfrac{(3b-1)(3b+1)}{(3b+1)^2}=\dfrac{3b-1}{3b+1}\).
\(\dfrac{b^5-b^4}{b^5-b^6}=\dfrac{b^4(b-1)}{b^5(1-b)}=-\dfrac1b\).
\(\dfrac{7m^2+7m+7}{m^3-1}=\dfrac{7(m^2+m+1)}{(m-1)(m^2+m+1)}=\dfrac7{m-1}\).
\(\dfrac{64-x^2}{3x^2-24x}=\dfrac{(8-x)(8+x)}{3x(x-8)}=-\dfrac{x+8}{3x}\).

Ответ: 1) \(\dfrac37\); 2) \(\dfrac{5}{2a}\); 3) \(\dfrac{x-4y}{4y}\); 4) \(\dfrac{x-7}{6}\); 5) \(-2a\); 6) \(\dfrac{3b-1}{3b+1}\); 7) \(-\dfrac1b\); 8) \(\dfrac7{m-1}\); 9) \(-\dfrac{x+8}{3x}\).