Правый столбец: упростить выражения 1) (7−3x)/x − (8−3y)/y; 2) (3a−8)/(5a) + (4a+6)/a; 3) (n+4)/(5n) − (m−2)/(5m); 4) x + (1+x²)/(1−x); 5) a−1+2/(a+1); 6) (1−3c)/(ac²) − (6−5c)/(ac); 7) x/y − 2/(x+y); 8) (a²+25)/(a−5) + 10a/(5−a).

Question

Вопрос:

Accepted Answer

\(\frac{7-3x}{x}-\frac{8-3y}{y}=\frac7x-\frac8y=\frac{7y-8x}{xy}\).
\(\frac{3a-8}{5a}+\frac{4a+6}{a}=\frac{3a-8+20a+30}{5a}=\frac{23a+22}{5a}\).
\(\frac{n+4}{5n}-\frac{m-2}{5m}=\frac{m(n+4)-n(m-2)}{5mn}=\frac{4m+2n}{5mn}\).
\(x+\frac{1+x^2}{1-x}=\frac{x(1-x)+1+x^2}{1-x}=\frac{x+1}{1-x}\).
\(a-1+\frac2{a+1}=\frac{(a-1)(a+1)+2}{a+1}=\frac{a^2+1}{a+1}\).
\(\frac{1-3c}{ac^2}-\frac{6-5c}{ac}=\frac{1-3c-c(6-5c)}{ac^2}=\frac{5c^2-9c+1}{ac^2}\).
\(\frac{x}{y}-\frac2{x+y}=\frac{x(x+y)-2y}{y(x+y)}=\frac{x^2+xy-2y}{y(x+y)}\).
Поскольку \(5-a=-(a-5)\), \(\frac{a^2+25}{a-5}-\frac{10a}{a-5}=\frac{a^2-10a+25}{a-5}=a-5\).

Ответ: 1) (7y−8x)/(xy); 2) (23a+22)/(5a); 3) (4m+2n)/(5mn); 4) (x+1)/(1−x); 5) (a²+1)/(a+1); 6) (5c²−9c+1)/(ac²); 7) (x²+xy−2y)/(y(x+y)); 8) a−5.