976. 1) \(\frac{ac-bc}{ac+bc}\) ; 2) \(\frac{ax+bx}{ax-bx}\) ; 3) \(\frac{a^2}{a^2+ab}\) ; 4) \(\frac{xy}{x-xy}\) ; 5) \(\frac{pq^3}{p^2q-pq^2}\) ; 6) \(\frac{ac-bc}{c^2+cd}\) ; 7) \(\frac{k^2+k}{kx-ky}\) ; 8) \(\frac{a^2+3ab}{a^2b+3ab^2}\)

Решение:

1. \(\frac{ac-bc}{ac+bc} = \frac{c(a-b)}{c(a+b)} = \frac{a-b}{a+b}\)

2. \(\frac{ax+bx}{ax-bx} = \frac{x(a+b)}{x(a-b)} = \frac{a+b}{a-b}\)

3. \(\frac{a^2}{a^2+ab} = \frac{a · a}{a(a+b)} = \frac{a}{a+b}\)

4. \(\frac{xy}{x-xy} = \frac{xy}{x(1-y)} = \frac{y}{1-y}\)

5. \(\frac{pq^3}{p^2q-pq^2} = \frac{pq^3}{pq(p-q)} = \frac{q^2}{p-q}\)

6. \(\frac{ac-bc}{c^2+cd} = \frac{c(a-b)}{c(c+d)} = \frac{a-b}{c+d}\)

7. \(\frac{k^2+k}{kx-ky} = \frac{k(k+1)}{k(x-y)} = \frac{k+1}{x-y}\)

8. \(\frac{a^2+3ab}{a^2b+3ab^2} = \frac{a(a+3b)}{ab(a+3b)} = \frac{1}{b}\)

Ответ: 1) \(\frac{a-b}{a+b}\); 2) \(\frac{a+b}{a-b}\); 3) \(\frac{a}{a+b}\); 4) \(\frac{y}{1-y}\); 5) \(\frac{q^2}{p-q}\); 6) \(\frac{a-b}{c+d}\); 7) \(\frac{k+1}{x-y}\); 8) \(\frac{1}{b}\).