Question

Simplificati fractia F(x)=(x la patrat+x+1)(x la patrat+x+2)-6 / ( x la patrat +x+2)( x la patrat +x+3)-2.

Answer 1

notam $x^{2} +x+1$ cu a.
=> f(x) devine $\frac{a(a+1)-6}{(a+1)(a+2)-2}$
=> f(x) = $\frac{ a^{2}+a-6 }{ a^{2} +3a}$
=> f(x) = $\frac{(a+3)(a-2)}{a(a+3)}$
=> f(x) = $\frac{a-2}{a}$
inlocuim a
=> f(x) = $\frac{ x^{2} +x-1}{ x^{2} +x+1}$