Nu prea am inteles ce inseamna DVA-ul, dar uite rezolvarea mea:
1)[tex] \frac{7x}{ x^{2} -25} = \frac{7x}{(x-5)(x+5)} [/tex]
2) (Aici trebuia sa inlocuim cu variantele date?)
[tex] \frac{ x^{2} -2}{3x+1} [/tex]
a) x=2
[tex] \frac{4-2}{6+1} = \frac{2}{7} [/tex]
b) x=[tex] \sqrt{3} [/tex]
[tex] \frac{3-2}{3 \sqrt{3} +1} = \frac{1}{3 \sqrt{3}+1 } [/tex]
Raționalizăm:
[tex] \frac{ 3\sqrt{3}-1}{(3 \sqrt{3}+1)(3 \sqrt{3}-1) } = \frac{3 \sqrt{3}-1 }{27-1} = \frac{3 \sqrt{3}-1}{26} [/tex]
3) a) (Aici e gresit: in loc de [tex] x^{2} +36[/tex] este [tex] x^{2} -36[/tex] )
[tex] \frac{ x^{2} -36}{ x^{2} +12x+36} = \frac{(x-6)(x+6)}{ (x+6)^{2} } = \frac{x-6}{x+6} [/tex]
b) [tex] \frac{ x^{2} -16}{ x^{2} -8x+16} = \frac{(x-4)(x+4)}{ (x-4)^{2} } = \frac{x+4}{x-4} [/tex]
