3. Упростите выражение: а) \(\frac{a^2-9b^2}{c^2+8cd+16d^2} \cdot \frac{c^2-16d^2}{3b-a}\) б) \(\frac{a^2-b^2+a+b}{x^2-y^2+x-y} \cdot \frac{3a+3b}{2x-2y}\)

Решение:

а) \(\frac{a^2-9b^2}{c^2+8cd+16d^2} \cdot \frac{c^2-16d^2}{3b-a} = \frac{(a-3b)(a+3b)}{(c+4d)^2} \cdot \frac{(c-4d)(c+4d)}{-(a-3b)} = \frac{(a+3b)(c-4d)}{-(c+4d)} = -\frac{(a+3b)(c-4d)}{c+4d}\)

б) \(\frac{a^2-b^2+a+b}{x^2-y^2+x-y} \cdot \frac{3a+3b}{2x-2y} = \frac{(a-b)(a+b)+(a+b)}{(x-y)(x+y)+(x-y)} \cdot \frac{3(a+b)}{2(x-y)} = \frac{(a+b)(a-b+1)}{(x-y)(x+y+1)} \cdot \frac{3(a+b)}{2(x-y)} = \frac{3(a+b)^2(a-b+1)}{2(x-y)^2(x+y+1)}\)

Ответ: а) -\(\frac{(a+3b)(c-4d)}{c+4d}\); б) \(\frac{3(a+b)^2(a-b+1)}{2(x-y)^2(x+y+1)}\).