14. Сократите дроби: 1) (9c + 27d)/(9c); 2) (6a − 18b)/(7a − 21b); 3) (a² − 64)/(3a + 24); 4) (20x² − 5x)/(6 − 24x); 5) (x² − 25)/(x² − 10x + 25); 6) (a⁵ − a⁷)/(a⁶ − a⁴); 7) (a³ − 216)/(2a − 12); 8) (3m² − 6m + 12)/(6m³ + 48); 9) (am − mb − 6a + 6b)/(m² − 36).

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Accepted Answer

\(\dfrac{9c+27d}{9c}=\dfrac{9(c+3d)}{9c}=\dfrac{c+3d}{c}\).
\(\dfrac{6a-18b}{7a-21b}=\dfrac{6(a-3b)}{7(a-3b)}=\dfrac67\), при \(a\ne3b\).
\(\dfrac{a^2-64}{3a+24}=\dfrac{(a-8)(a+8)}{3(a+8)}=\dfrac{a-8}{3}\), при \(a\ne-8\).
\(\dfrac{20x^2-5x}{6-24x}=\dfrac{5x(4x-1)}{6(1-4x)}=-\dfrac{5x}{6}\), при \(x\ne\dfrac14\).
\(\dfrac{x^2-25}{x^2-10x+25}=\dfrac{(x-5)(x+5)}{(x-5)^2}=\dfrac{x+5}{x-5}\), при \(x\ne5\).
\(\dfrac{a^5-a^7}{a^6-a^4}=\dfrac{a^5(1-a^2)}{a^4(a^2-1)}=-a\), при \(a\ne0,\pm1\).
\(\dfrac{a^3-216}{2a-12}=\dfrac{(a-6)(a^2+6a+36)}{2(a-6)}=\dfrac{a^2+6a+36}{2}\), при \(a\ne6\).
\(\dfrac{3m^2-6m+12}{6m^3+48}=\dfrac{3(m^2-2m+4)}{6(m+2)(m^2-2m+4)}=\dfrac{1}{2(m+2)}\), при \(m\ne-2\).
\(\dfrac{am-mb-6a+6b}{m^2-36}=\dfrac{(a-b)(m-6)}{(m-6)(m+6)}=\dfrac{a-b}{m+6}\), при \(m\ne\pm6\).

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