100. Упростите выражение: 1) (a+7)/12 + (a−4)/9; 2) (2b−7c)/6 − (3b+2c)/15; 3) (3x−2)/x − (3y−1)/y; 4) (6p+1)/p − (2p+8)/(3p); 5) (5m−n)/(14m) − (m−6n)/(7m); 6) (x+4)/(11x) − (y−3)/(11y); 7) (a+b)/(ab) + (a−c)/(ac); 8) 2/p² + (p−1)/p; 9) (k+4)/k − (3k−4)/k²; 10) (x−y)/x³ − (y−x²)/(x²y); 11) (2m−3n)/(m²n) + (7m−2n)/(mn²); 12) (c+d)/(cd⁴) − (c²−8d)/(c³d³).

Question

Вопрос:

Фото задания: 100. Упростите выражение: 1) (a+7)/12 + (a−4)/9; 2) (2b−7c)/6 − (3b+2c)/15; 3) (3x−2)/x − (3y−1)/y; 4) (6p+1)/p −…

100. Упростите выражение: 1) (a+7)/12 + (a−4)/9; 2) (2b−7c)/6 − (3b+2c)/15; 3) (3x−2)/x − (3y−1)/y; 4) (6p+1)/p − (2p+8)/(3p); 5) (5m−n)/(14m) − (m−6n)/(7m); 6) (x+4)/(11x) − (y−3)/(11y); 7) (a+b)/(ab) + (a−c)/(ac); 8) 2/p² + (p−1)/p; 9) (k+4)/k − (3k−4)/k²; 10) (x−y)/x³ − (y−x²)/(x²y); 11) (2m−3n)/(m²n) + (7m−2n)/(mn²); 12) (c+d)/(cd⁴) − (c²−8d)/(c³d³).

Accepted Answer

Приводим дроби к общему знаменателю, объединяем числители и сокращаем, где возможно.

\(\frac{3(a+7)+4(a-4)}{36}=\frac{7a+5}{36}\).
\(\frac{5(2b-7c)-2(3b+2c)}{30}=\frac{4b-39c}{30}\).
\(3-\frac2x-3+\frac1y=\frac{x-2y}{xy}\).
\(\frac{3(6p+1)-(2p+8)}{3p}=\frac{16p-5}{3p}\).
\(\frac{5m-n-2(m-6n)}{14m}=\frac{3m+11n}{14m}\).
\(\frac{y(x+4)-x(y-3)}{11xy}=\frac{4y+3x}{11xy}\).
\(\frac{c(a+b)+b(a-c)}{abc}=\frac{a(b+c)}{abc}=\frac{b+c}{bc}\).
\(\frac{2+p(p-1)}{p^2}=\frac{p^2-p+2}{p^2}\).
\(\frac{k(k+4)-(3k-4)}{k^2}=\frac{k^2+k+4}{k^2}\).
\(\frac{y(x-y)-x(y-x^2)}{x^3y}=\frac{x^3y+xy-y^2}{x^3y}\).
\(\frac{n(2m-3n)+m(7m-2n)}{m^2n^2}=\frac{7m^2-2mn+2mn-3n^2}{m^2n^2}=\frac{7m^2-3n^2}{m^2n^2}\).
\(\frac{c^2(c+d)-d(c^2-8d)}{c^3d^4}=\frac{c^3+c^2d-c^2d+8d^2}{c^3d^4}=\frac{c^3+8d^2}{c^3d^4}\).

Ответ: 1) (7a+5)/36; 2) (4b−39c)/30; 3) (x−2y)/(xy); 4) (16p−5)/(3p); 5) (3m+11n)/(14m); 6) (3x+4y)/(11xy); 7) (b+c)/(bc); 8) (p²−p+2)/p²; 9) (k²+k+4)/k²; 10) (x³y+xy−y²)/(x³y); 11) (7m²−3n²)/(m²n²); 12) (c³+8d²)/(c³d⁴).