3. Упростите выражение: 1) x − 1/x; 2) (5b + 1)/(b + 2) − 4; 3) 4/a² + 5/y − 7; 4) (5b + 1)/(b² + 2) − 4; 5) (m² − n²)/(m + 3n) + m − 3n; 6) x − 9/(x − 3) − 3.

Question

Вопрос:

Accepted Answer

\(x-\frac1x=\frac{x^2-1}{x}\), \(x\ne0\).
\(\frac{5b+1}{b+2}-4=\frac{5b+1-4(b+2)}{b+2}=\frac{b-7}{b+2}\), \(b\ne-2\).
Общий знаменатель — \(a^2y\): \(\frac4{a^2}+\frac5y-7=\frac{4y+5a^2-7a^2y}{a^2y}\), \(a\ne0, y\ne0\).
\(\frac{5b+1}{b^2+2}-4=\frac{5b+1-4(b^2+2)}{b^2+2}=\frac{-4b^2+5b-7}{b^2+2}\).
\(\frac{m^2-n^2}{m+3n}+m-3n=\frac{m^2-n^2+(m-3n)(m+3n)}{m+3n}=\frac{2(m^2-5n^2)}{m+3n}\), \(m+3n\ne0\).
\(x-\frac9{x-3}-3=(x-3)-\frac9{x-3}=\frac{(x-3)^2-9}{x-3}=\frac{x(x-6)}{x-3}\), \(x\ne3\).

Ответ: