Question

simplificati fractia x la puterea a doua minus 1 supra x la puterea 2 minus 3x minus 4 egal cu x la puterea 2 minus 1 la puterea 2 supra x la puterea 2 minus 5

Answer 1

$\frac{ x^{2} -1}{ x^{2} -3x-4} = \frac{ x^{2} - 1^{2} }{ x^{2}-5 }$
$\frac{ x^{2} -1}{ x^{2} -3x-4} = \frac{ x^{2} - 1^{2} }{ x^{2}-5 }, x \neq 4,x \neq -1,x \neq \sqrt{5 },$x≠-√5
$\frac{(x-1)*(x+1)}{ x^{2} +x-4x-4} = \frac{ x^{2} -1}{ x^{2} -5}$
$\frac{(x-1)*(x+1)}{ x*( x+1)-4(x+1)} = \frac{ x^{2} -1}{ x^{2} -5}$
$\frac{(x-1)*(x+1)}{(x-4)*(x+1)} =\frac{ x^{2} -1}{ x^{2} -5}$
$\frac{x-1}{x-4} =\frac{ x^{2} -1}{ x^{2} -5}$
(x-1)*(x²-5)=(x²-1)*(x-4)
(x-1)*(x²-5)-(x²-1)*(x-4)=0
x³-5x-x²+5-(x³-4x²-x+4)=0
x³-5x-x²+5-x³+4x²+x-4=0
-4x+3x²+1=0
3x²-4x+1=0
$x= \frac{-(-4)+ \sqrt{(-4) ^{2}-4*3*1 } }{2*3}$
$x= \frac{4+ \sqrt{16-12} }{6}$
$x= \frac{4+ \sqrt{4} }{6}$
$x= \frac{4+2}{6}$
$x= \frac{4-2}{6}$
x=1
$x= \frac{1}{3}, x \neq 4, x \neq -1, x \neq \sqrt{5}, x=- \sqrt{5}$