Question

10. Simplificati rapoartele:1)x²+x-2 supra x²+2x-3
2)x²+x-6 supra x²+2x-8
3)x²+5x-14 supra x²+4x-21

Answer 1

1) x²+x-2 supra x²+2x-3=(x+2)(x-1) supra (x+3)(x-1)=x+2 supra x+3
2) x²+x-6 supra x²+2x-8=(x-2)(x+3) supra (x-2)(x+4)=x+3 supra x+4
3) x²+5x-14 supra x²+4x-21=(x+7)(x-2) supra (x+7)(x-3)=x-2 supra x-3

Answer 2

$\frac{ x^{2} +x-2}{ x^{2} +2x-3}= \frac{ x^{2} +x-2+ \frac{9}{4}- \frac{9}{4} }{ x^{2} +2x-3+4-4} = \frac{(x+ \frac{1}{2})^2- \frac{9}{4} }{ (x+1)^{2}-4 } = \frac{(x+ \frac{1}{2} - \frac{3}{2})(x+ \frac{1}{2}+ \frac{3}{2} ) }{(x+1-2)(x+1+2)} = \frac{(x-1)(x+2)}{(x-1)(x+3}=$=$\frac{x+2}{x+3}$...sper sa intelegi de unde a venit rezultatul :)