Question

Помогите упростить выражения.Если есть возможность - с объяснением, как можно подробней)Заранее спасибо!

Answer 1

1)ax²-bx²-bx+ax-a+b=x²(a-b)+x(a-b)-(a-b)=(a-b)(x²+x-1)

2)(2x+3) -(x-1)²=(2x+3-x+1)(2x+3+x-1)=(x+4)(3x+2)

3)x²+2xy+y²-1=(x+y)²-1=(x+y-1)(x+y+1)

4)[(3a+2)/(3a²+1) -(18a³-a-9)/(9a^4 -1) +(3a-2)/(3a²-1)] :(a²+10a+25)/(9a^4 -1)=
=1/(a+5)
1)(3a+2)/(3a²+1) -(18a³-a-9)/(9a^4 -1) +(3a-2)/(3a²-1)=
=(9a³+6a²-3a-2-18a³+a+9+9a³+3a-6a²-2)/(9a^4-1)=(a+5)/(9a^4 -1)
2)(a+5)/(9a^4 -1) : (a²+10a+25)/(9a^4 -1)=(a+5)/(9a^4 -1)*(9a^4 -1)/(a+5)²=1/(a+5)

5)[(2x²y+2xy²)/(7x³+x²y+7xy²+y³) * (7x+y)/(x²-y²) +(x-y)/(x²+y²)]*(x²-y²)=1/(x-y)
1)(2x²y+2xy²)/(7x³+x²y+7xy²+y³) * (7x+y)/(x²-y²)=
=2xy(x+y)/[x²(7x+y) +y²(7x+y)]* (7xy/(x²-y²)=2xy(x+y)/(x²+y²)(7x+y) * (7x+y)/(x²-y²)=
=2xy(x+y)/(x²+y²)(7x+y) * (7x+y)/(x-y)(x+y)=2xy/(x²+y²)(x-y)
2)2xy/(x²+y²)(x-y)+(x-y)/(x²+y²)=(2xy+x²-2xy+y²)/(x²+y²)(x-y)=(x²+y²)/(x²+y²)(x-y)=
=1/(x-y)

6)[2/(m+n)³ * (1/m +1/n) +1/(m²+2mn+n²) * (1/m²+1/n²)]:(m-n)/(m³+n³)=mn/(m-n)
1)1/m+1/n=(n+m)/mn
2)2/(m+n)³*(n+m)/mn=2/mn(m+n)²
3)1/m²+1/n²=(m²+n²)/m²n²
4)1/(m²+2mn+n²)*(m²+n²)/m²n²=1/(m+n)²*(m²+n²)/m²n²=(m²+n²)/m²n²(m+n)²
5)2/mn(m+n)² + (m²+n²)/m²n²(m+n)²=(2mn+m²+n²)/m²n²(m+n)²=(m+n)²/m²n²(m+n)²=
=1/m²n²
6)1/m²n² : (m-n)/m³n³=1/m²n² *m³n³/(m-n)=mn/(m-n)

Answer 2

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