Помогите! Сократить дробь; 1) a^4-b^4/a^3-b^3 2) 3n^2-3m^2/6m^3+6n^3 4)a^4-b^4/a^2-b^2...

Question

Помогите! Сократить дробь;
1) a^4-b^4/a^3-b^3
2) 3n^2-3m^2/6m^3+6n^3
4)a^4-b^4/a^2-b^2
5)x^6+x^4/x^4+x^2
6) X^6-x^8/x^4-x^2
7)m^7-m^10/m^9-m^3
8) a^6-a^4/a^3+a^2

Answer 1

1) a^4-b^4/a^3-b^3=(a-b)(a+b)(a²+b²)/(a-b)(a²+ab+b²)=
=(a+b)(a²+b²)/(a²+ab+b²)
2) 3n^2-3m^2/6m^3+6n^3=3(n-m)(n+m)/6(m+n)(m²-mn+n²)=
=(n-m)/2(m²-mn+n²)
4)a^4-b^4/a^2-b^2=(a²-b²)(a²+b²)/(a²-b²)=a²+b²
5)x^6+x^4/x^4+x^2=x^4(x²+1)/x²(x²+1)=x²
6) X^6-x^8/x^4-x^2=x^6(1-x²)/x²(x²-1)=-x^4
7)m^7-m^10/m^9-m^3=m^7(1-m³)/m³(m³-1)(m³+1)=-m^4/(m³+1)
8) a^6-a^4/a^3+a^2=a^4(a-1)(a+1)(a²+1)/a²(a+1)=a²(a-1)(a²+1)