Question

calcule $\frac{x^2-1}{x^2+2x+1} = \frac{13}{17}$

Answer 1

$\frac{ x^{2} -1}{ x^{2} +2x+1}= \frac{13}{17}\\ \\ Multiplicando~cruzado,~temos:\\\\ 17( x^{2} -1)=13( x^{2} +2x+1)\\ 17 x^{2} -17=13 x^{2} +26x+13\\ 17 x^{2} -13 x^{2} -26x-17-13=0\\\\ 4 x^{2} -26x-30=0~~:2\\ 2 x^{2} -13x-15=0\\\\ Por~Baskara,~temos:\\ \\ \boxed{\Delta=b ^{2}-4ac}~\to~\Delta=(-13) ^{2}-4*2*(-15)~\to~\Delta=289$

$\boxed{x= \frac{-b\pm \sqrt{\Delta} }{2a}}\\\\\\ x= \frac{-(-13)\pm \sqrt{289} }{2*2}~\to~x=\frac{13\pm17}{4}\begin{cases}x'= \frac{13-17}{4}~\to~x'= \frac{-4}{4}~\to~x=-1\\\\ x''= \frac{13+17}{4}~\to~x''= \frac{30}{4}~\to~x''= \frac{15}{2} \end{cases} \\\\\\\\ \boxed{\boxed{S=\{-1, \frac{15}{2}\}}}$


Espero ter ajudado e tenha ótimos estudos ;D