((3/(n+1)!-2/n!))/((4/n!)-(3n)/(n+1)!)

Question

((3/(n+1)!-2/n!))/((4/n!)-(3n)/(n+1)!)

Answer 1

((3/(n+1)!-2/n!))/((4/n!)-(3n)/(n+1)!)=

=(3n!-2(n+1)!)/(n!(n+1)! : (4(n+1)!-3n*n!)/(n!(n+1)!)=

=(3n!-2n!(n+1)!)/(n!(n+1)!) *(n!(n+1)!)/(4n!(n+1)-3n*n!))=

=n!(3-2(n+1))/((n!(4(n+1)-3n))=

=(3-2n-2)/(4n+4-3n)=(1-2n)/(n+4)