Question

(1/4+1/3)/(2/3-2/5)= x/(1/4+1/2)

Answer 1

$\dfrac{\frac{1}{4}+\frac{1}{3}}{\frac{2}{3}-\frac{2}{5}}=\dfrac{x}{\frac{1}{4}+\frac{1}{2}}$


Para somar/subtrair frações com denominadores diferentes, devemos reduzi-las ao mesmo denominador comum:

$=\dfrac{\frac{3}{12}+\frac{4}{12}}{\frac{10}{15}-\frac{6}{15}}=\dfrac{x}{\frac{1}{4}+\frac{2}{4}}\\\\\\ =\dfrac{~~\frac{7}{12}~~}{\frac{4}{15}}=\dfrac{~~x~~}{\frac{3}{4}}$


Agora, multiplica os meios e os extremos ("em cruz") e obtemos,

$\dfrac{4}{15}\,x=\dfrac{7}{12}\cdot \dfrac{3}{4}\\\\\\ \dfrac{4x}{15}=\dfrac{21}{48}$


Multiplicando os meios e os extremos ("em cruz") novamente, obtemos,

$4x\cdot 48=15\cdot 21\\\\ 192x=315\\\\ x=\dfrac{315}{192}\begin{array}{l}^{\div 3}\\^{\div 3} \end{array}\\\\\\ \therefore~~\boxed{\begin{array}{c} x=\dfrac{105}{64} \end{array}}$


Bons estudos! :-)