Question

Fie fractia Fx=2xla a3a +xla a 2a -xtotul supra x la a2a+x.
a)Simplificati fractia.

Answer 1

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Answer 2

$F= \frac{2 x^{3}+ x^{2} -x }{ x^{2} +x} = \\ = \frac{2 x^{3}-2x+ x^{2}+x }{x(x+1)}= \\ = \frac{2x( x^{2} -1)+x(x+1)}{x(x+1)}= \\ = \frac{2x(x+1)(x-1)+x(x+1)}{x(x+1)}= \\ = \frac{x(x+1)[2(x-1)+1]}{x(x+1)}= \\ = 2(x-1)+1= \\ =\boxed{2x-1}.$