70. Упростите выражение: 1) a²/(a+3) − 9/(a+3); 2) t/(t²−16) − 4/(t²−16); 3) m²/(m−5)² − 25/(m−5)²; 4) (5x+9)/(x²−1) − (4x+8)/(x²−1); 5) b²/(b+10) + (20b+100)/(b+10); 6) c²/(c−7) − (14c−49)/(c−7).

Question

Вопрос:

Accepted Answer

\(\frac{a^2-9}{a+3}=\frac{(a-3)(a+3)}{a+3}=a-3\).
\(\frac{t-4}{t^2-16}=\frac{t-4}{(t-4)(t+4)}=\frac1{t+4}\).
\(\frac{m^2-25}{(m-5)^2}=\frac{(m-5)(m+5)}{(m-5)^2}=\frac{m+5}{m-5}\).
\(\frac{5x+9-4x-8}{x^2-1}=\frac{x+1}{(x-1)(x+1)}=\frac1{x-1}\).
\(\frac{b^2+20b+100}{b+10}=\frac{(b+10)^2}{b+10}=b+10\).
\(\frac{c^2-14c+49}{c-7}=\frac{(c-7)^2}{c-7}=c-7\).

Ответ: 1) \(a-3\); 2) \(\frac1{t+4}\); 3) \(\frac{m+5}{m-5}\); 4) \(\frac1{x-1}\); 5) \(b+10\); 6) \(c-7\).