Question

5/x+4/x+1=7/12
/ = sobre favor deixar calculo

Answer 1

Olá Duda,

para facilitar, multiplique cruzado e faça as somas, multiplicando os denominadores também:

$\dfrac{5}{x}+ \dfrac{4}{x+1}= \dfrac{7}{12}~\to~ \dfrac{5*(x+1)+4*x}{x*(x+1)}= \dfrac{7}{12}\\\\\\ ~\to~ \dfrac{5x+5+4x}{ x^{2} +x}= \dfrac{7}{12}~\to~ \dfrac{9x+5}{ x^{2} +x}= \dfrac{7}{12}\\\\\\ ~\to~7( x^{2} +x)=12(9x+5)~\to~7 x^{2} +7x=108x+60\\\\ ~\to~7 x^{2} +7x-108x-60=0~\to~7 x^{2} -101x-60=0$

$\Delta=b^2-4ac\\ \Delta=(-101)^2-4*7*(-60)\\ \Delta=10.201+1.680\\ \Delta=11.881$

$x= \dfrac{-b\pm \sqrt{\Delta} }{2a}= \dfrac{-(-101)\pm \sqrt{11.881} }{2*7}= \dfrac{101\pm109}{14}\\\\\\ ~\to~\begin{cases}x'= \dfrac{101+109}{14}= \dfrac{210}{14} =15\\\\ x''= \dfrac{101-109}{14}= \dfrac{-8}{~14}= \dfrac{-8:2}{~14:2}=- \dfrac{4}{7}\end{cases}\\\\\\ S=\left\{15,- \dfrac{4}{7}\right\}$

Espero ter ajudado e tenha ótimos estudos =))