В. Упростите дроби: 1) −(x+y)/(x+y); 2) −2(a+b)/(a+b); 3) (x+3)/(−5(x+3)); 4) 2(b+1)/(−(b+1)); 5) −(x−3)/(12(x−3)); 6) (a+5)(a+5)/((5+a)(5−a)); 7) (13+x)/((x+13)·b); 8) −(y−1)/(−(−1+y)); 9) 2(a−b)/(3(b−a)); 10) 5(x−y)/(a(y−x)); 11) x(y+3)/(2(−y−3)); 12) 5(−2+a)/(3(a−2)); 13) (y−1)/(3(−1+y)); 14) a(a−1)/(−(1−a)); 15) (y−1)(y−1)/((1−y)(1+y)); 16) (y+1)(y−1)/(−y−1); 17) −2(a−b)/(a−b)²; 18) (x−3)/(3−x)²; 19) (b−1)²/((1−b)(1+b)); 20) (a+3)(a−3)/(3−a)²; 21) (y−2)(y+2)/(2+y)²; 22) −(a−2)/((2−a)(a+2)); 23) (x−1)(x+1)/((1−x)(−x−1)); 24) −(x−1)(1−x)/(x−1)².

Question

Вопрос:

Фото задания

В. Упростите дроби: 1) −(x+y)/(x+y); 2) −2(a+b)/(a+b); 3) (x+3)/(−5(x+3)); 4) 2(b+1)/(−(b+1)); 5) −(x−3)/(12(x−3)); 6) (a+5)(a+5)/((5+a)(5−a)); 7) (13+x)/((x+13)·b); 8) −(y−1)/(−(−1+y)); 9) 2(a−b)/(3(b−a)); 10) 5(x−y)/(a(y−x)); 11) x(y+3)/(2(−y−3)); 12) 5(−2+a)/(3(a−2)); 13) (y−1)/(3(−1+y)); 14) a(a−1)/(−(1−a)); 15) (y−1)(y−1)/((1−y)(1+y)); 16) (y+1)(y−1)/(−y−1); 17) −2(a−b)/(a−b)²; 18) (x−3)/(3−x)²; 19) (b−1)²/((1−b)(1+b)); 20) (a+3)(a−3)/(3−a)²; 21) (y−2)(y+2)/(2+y)²; 22) −(a−2)/((2−a)(a+2)); 23) (x−1)(x+1)/((1−x)(−x−1)); 24) −(x−1)(1−x)/(x−1)².

Accepted Answer

При сокращении учитываем равенства противоположных выражений, например: \(b-a=-(a-b)\), \(3-x=-(x-3)\), \(1-x=-(x-1)\).

−1
−2
−1/5
−2
−1/12
\(\dfrac{a+5}{5-a}\)
\(\dfrac1b\)
1
−2/3
−5/a
−x/2
5/3
1/3
a
\(\dfrac{1-y}{y+1}\)
1−y
\(\dfrac{-2}{a-b}\)
\(\dfrac1{x-3}\)
\(\dfrac{1-b}{b+1}\)
\(\dfrac{a+3}{a-3}\)
\(\dfrac{y-2}{y+2}\)
\(\dfrac1{a+2}\)
1
1

Ограничения: сокращение допустимо только при ненулевых исходных знаменателях и сокращаемых множителях.

Ответ: 1) −1; 2) −2; 3) −1/5; 4) −2; 5) −1/12; 6) \(\dfrac{a+5}{5-a}\); 7) \(\dfrac1b\); 8) 1; 9) −2/3; 10) −5/a; 11) −x/2; 12) 5/3; 13) 1/3; 14) a; 15) \(\dfrac{1-y}{y+1}\); 16) 1−y; 17) \(\dfrac{-2}{a-b}\); 18) \(\dfrac1{x-3}\); 19) \(\dfrac{1-b}{b+1}\); 20) \(\dfrac{a+3}{a-3}\); 21) \(\dfrac{y-2}{y+2}\); 22) \(\dfrac1{a+2}\); 23) 1; 24) 1.