Question

Como fazer isso:
((x+1)/(x+2))+1/((x+1)/(x+2))
Virar isso:
(2x²+6x+5)/((x+2)/(x+1))

Answer 1

$\dfrac{x+1}{x+2}+\dfrac{1}{\dfrac{x+1}{x+2}}\ (1\ sobre\ algo\ \'e\ a\ inversa,\ pode\ ser\ invertido)\\\\\\ \dfrac{x+1}{x+2}+\dfrac{x+2}{x+1}\ (tiramos\ o\ m.m.c.)\\\\ \dfrac{(x+1)^2+(x+2)^2}{(x+2)(x+1)}\ (Encontrando\ o\ trin\^omio)\\\\ \dfrac{x^2+2x+1+x^2+4x+4}{(x+2)(x+1)}\\\\ \boxed{\boxed{\dfrac{2x^2+6x+5}{(x+2)(x+1)}}}$

Bons estudos!