Упростите выражение

(3m-3n)/(m^3-n^3)

(a^2-4a+4)/(a^2-4)

(6a^2-6b^2)/(3a^3+3b^3)

(1-a^3)/(1+a+a^2)

(x^3-y^3)/(x^2-y^2)

(2p^2-2p+2)/(p^3+1)

(m^2-n^2)/(m^3-n^3)

(2p^3-2q^3)/(4q^2-4p^2)

((x^3-y^3)(x+y))/(x^2-y^2)

Решение:

(3m-3n)/(m^3-n^3 )=(3(m-n))/((m-n)(m^2+mn+n^2))=3/(m^2+mn+n^2 )

(a^2-4a+4)/(a^2-4)=((a-2)^2)/((a-2)(a+2))=(a-2)/(a+2)

(6a^2-6b^2)/(3a^3+3b^3 )=(6(a-b)(a+b))/(3(a+b)(a^2-ab+b^2))=(2a-2b)/(a^2-ab+b^2 )

(1-a^3)/(1+a+a^2)=((1-a)(1+a+a^2))/(1+a+a^2 )=1-a

(x^3-y^3)/(x^2-y^2)=((x-y)(x^2+xy+y^2))/((x-y)(x+y))=(x^2+xy+y^2)/(x+y)

(2p^2-2p+2)/(p^3+1)=(2(p^2-p+1))/((p+1)(p^2-p+1))=( 2)/(p+1)

(3x^2+6xy+3y^2)/(12y^2-12x^2 )=(3(x+y)^2)/(12(y+x)(y-x))=(x+y)/(4y-4x)

(m^2-n^2)/(m^3-n^3)=((m-n)(m+n))/((m-n)(m^2+mn+n^2))=(m+n)/(m^2+mn+n^2 )

(2p^3-2q^3)/(4q^2-4p^2)=(2(p-q)(p^2+pq+q^2))/(4(q-p)(q+p))=(-2(q-p)(p^2+pq+q^2))/(4(q-p)(q+p))=(-p^2-pq-q^2)/(2q+2p)

((x^3-y^3)(x+y))/(x^2-y^2)=((x-y)(x^2+xy+y^2)(x+y))/((x-y)(x+y))=x^2+xy+y^2