Ответы
Ответ:
Объяснение:
1.
(4x)/y³ ·y/(20x²)=1/(5xy²)
(x²-16)/(x-3) ·(x²-6x+9)/(2x-8)=((x-4)(x+4))/(x-3) ·(x-3)²/(2(x-4))=((x+4)(x-3))/2=(x²-3x+4x-12)/2=(x²+x-12)/2
(2x³)/(15y⁴) ÷(20x⁸)/(27y⁶)=(2x³)/(3·5y⁴) ·(3³y⁶)/(2²·5x⁸)=(3²y²)/(5²x⁵)=(9y²)/(25x⁵)
(m²+5m)/(16m²-1) ÷(m⁴+125m)/(16m²-8m+1)=(m(m+5))/((4m-1)(4m+1)) ·(4m-1)²/(m(m³+5³))=(m+5)/(4m+1) ·(4m-1)/((m+5)(m²-5m+25))=(4m-1)/((4m+1)(m²-5m+25))=(4m-1)/(4m³-20m²+100m+m²-5m+25)=(4m-1)/(4m³-19m²+95m+25)
2.
(x²-25)/(x+5)=0
x+5≠0; x₁≠-5
x²-25=0
(x-5)(x+5)=0
x-5=0; x₂=5
x+5=0; x₃=-5 - этот корень не подходит для этого уравнения, так как x₁≠-5.
Ответ: 5.
(x-1)/(x+5) +2=0
(x-1)/(x+5) +(2(x+5))/(x+5)=0
(x-1+2x+10)/(x+5)=0
(3x+9)/(x+5)=0
(3(x+3))/(x+5)=0
x+5=0; x₁≠-5
x+3=0; x₂=-3
Ответ: -3.
3.
((a-2)/(a+2) -(a+2)/(a-2)) ÷(12a²)/(4-a²)=((a-2)²-(a+2)²)/((a+2)(a-2)) ·((a-2)(a+2))/(-12a²)=(a²-4a+4-a²-4a-4)/(-12a²)=(-8a)/(-12a²)=2/(3a)
((3m)/(m+5) -(8m)/(m²+10m+25)) ÷(3m+7)/(m²-25) +(5m-25)/(m+5)=((3m)/(m+5) -(8m)/(m+5)²) ·((m-5)(m+5))/(3m+7) +(5(m-5))/(m+5)=(3m(m+5)-8m)/(m+5) ·(m-5)/(3m+7) +(5(m-5))/(m+5)=(3m²+15m-8m)/(m+5) ·(m-5)/(3m+7) +(5(m-5))/(m+5)=(m(3m+7))/(m+5) ·(m-5)/(3m+7) +(5(m-5))/(m+5)=(m(m-5))/(m+5) +(5(m-5))/(m+5)=(m(m-5)+5(m-5))/(m+5)=((m-5)(m+5))/(m+5)=m-5