Question

$Efectuati: \\ a) \frac{x}{x+1} + \frac{x}{ x^{2} +x} \\ b) \frac{y+2}{4y+6} + \frac{2y+4}{2y+3} \\ c) \frac{n+1}{n+2}* \frac{n+2}{n+3} : \frac{n+1}{n+3} \\ d) \frac{2m+3}{6p+4} : \frac{4m+6}{9p+6} + \frac{3n+3}{8q+20} * \frac{2q+1}{3(n+1)}$

Answer 1

a)
x/(x+1)+x(x²+x)=
=x/(x+1)+x/x(x+1)=
=x/(x+1)+1/(x+1)=
=(x+1)/(x+1)=1
b)
(y+2)/(4y+6)+(2y+4)/(2y+3)=
=(y+2)/2(2y+3)+2(y+2)/(2y+3)=
[(y+2)/(2y+3)]*(1/2+2)=
=5/2[(y+2)/(2y+3)]=
=5(y+2)/2(2y+3)=(5y+10)/(4y+6)
c)
(n+1)(n+2)/(n+2)(n+3):(n+1)/(n+3)=
=(n+1)/(n+3)*(n+3)/(n+1)=
=(n+1)(n+3)/(n+3)/(n+1)=1
d)
(2m+3)/(6q+4):(4m+6)/(9q+6) + (3n+3)*(2q+1)/(8q+20)*3(n+1)=
=(2m+3)*3(3q+2)/2(3q+2)*2(2m+3) + (2p+1)/(8q+20)=
=3/4+(2p+1)/(8q+20)=
=3(8q+20)+(2q+1)/4(8q+20)=
=(24q+60+2q+1)/(32q+80)=(26q+61)/(32q+80)