124. Упростите выражение: а) (y^2-16)/(10xy) * (5y)/(3y+12); б) (b-a)/a * (3ab)/(a^2-b^2)

### 124 а) $\frac{y^2-16}{10xy} \cdot \frac{5y}{3y+12} = \frac{(y-4)(y+4)}{10xy} \cdot \frac{5y}{3(y+4)} = \frac{y-4}{6x}$ б) $\frac{b-a}{a} \cdot \frac{3ab}{a^2-b^2} = \frac{-(a-b)}{a} \cdot \frac{3ab}{(a-b)(a+b)} = -\frac{3b}{a+b}$ ### 125 а) $\frac{a^2-1}{a-b} \cdot \frac{7a-7b}{a^2+a} = \frac{(a-1)(a+1)}{a-b} \cdot \frac{7(a-b)}{a(a+1)} = \frac{7(a-1)}{a} = \frac{7a-7}{a}$ б) $\frac{b^2+2bc}{b+3} \cdot \frac{5b+15}{b^2-4c^2} = \frac{b(b+2c)}{b+3} \cdot \frac{5(b+3)}{(b-2c)(b+2c)} = \frac{5b}{b-2c}$ в) $\frac{(x+3)^2}{2x-4} \cdot \frac{x^2-4}{3x+9} = \frac{(x+3)^2}{2(x-2)} \cdot \frac{(x-2)(x+2)}{3(x+3)} = \frac{(x+3)(x+2)}{6} = \frac{x^2+5x+6}{6}$ г) $\frac{(5-y)^2}{2y+12} \cdot \frac{y^2-36}{2y-10} = \frac{(5-y)^2}{2(y+6)} \cdot \frac{(y-6)(y+6)}{2(y-5)} = \frac{(y-5)^2(y-6)}{4(y-5)} = \frac{(y-5)(y-6)}{4} = \frac{y^2-11y+30}{4}$ ### 126 а) Выражение: $\frac{5mn-m}{4m+n} \cdot \frac{16m^2-n^2}{5n-1} = \frac{m(5n-1)}{4m+n} \cdot \frac{(4m-n)(4m+n)}{5n-1} = m(4m-n) = 4m^2-mn$. При $m=0.25$ и $n=-3$: $4 \cdot (0.25)^2 - 0.25 \cdot (-3) = 0.25 + 0.75 = 1$. б) Выражение: $\frac{(x+2)^2}{3x+9} \cdot \frac{2x+6}{x^2-4} = \frac{(x+2)^2}{3(x+3)} \cdot \frac{2(x+3)}{(x-2)(x+2)} = \frac{2(x+2)}{3(x-2)}$. При $x=0.5$: $\frac{2(2.5)}{3(-1.5)} = \frac{5}{-4.5} = -\frac{10}{9} = -1\frac{1}{9}$. При $x=-1.5$: $\frac{2(0.5)}{3(-3.5)} = \frac{1}{-10.5} = -\frac{2}{21}$.