Question

Aflati DVA al perechilor de fractii algebrice:
\frac{(X+4) ^{2 } }{X ^{2}+4X } + \frac{(X-4) ^{2} }{X ^{2}-4X }
\frac{3-X ^{2} }{9-X ^{2} } + \frac{X+3}{X-3}

Answer 1

1) [tex] \frac{ (x+4)^{2} }{ x^{2} +4x} + \frac{ (x-4)^{2} }{ x^{2} -4x} = \frac{ (x+4)^{2} }{ x(x +4)}+ \frac{ (x-4)^{2} }{ x(x -4)}= \frac{x+4}{x} + \frac{x-4}{x} = \frac{2x}{x} =2 [/tex]

2) [tex] \frac{ x^{2} -3}{ x^{2} -9} + \frac{x+3}{x-3} = \frac{x^{2} -3}{(x-3)(x+3)} +\frac{x+3}{x-3} = \frac{x^{2} -3}{(x-3)(x+3)} +\frac{(x+3)(x+3)}{(x-3)(x+3)} = [/tex]$=\frac{ x^{2}-3+ x^{2} +6x+9}{ x^{2} -9} = \frac{2 x^{2} +6x+6} { x^{2} -9}$