Question

Simplificati rapoartele si aflati domeniul lor de definiti x la puterea 2 -6x-16 supra x la puterea 2 -5x-14

Answer 1

b) $\frac{2x^{3}- x^{2} -2x+1 }{2x^{3}+ x^{2} -2x-1}= \frac{ x^{2} *(2x-1)-(2x-1)}{x^{2} *(2x+1)-(2x+1)}= \frac{( x^{2} -1)*(2x-1)}{( x^{2} -1)*(2x+1)}= \frac{(x-1)*(x+1)*(2x-1)}{(x-1)*(x+1)*(2x+1)}$$= \frac{2x-1}{2x+1}$

e)$\frac{x^{3}- x^{2} -9x+9 }{x^{3}+ x^{2} -9x-9}= \frac{ x^{2} *(x-1)-9(x-1)}{x^{2} *(x+1)-9(x+1)}= \frac{( x^{2} -9)*(x-1)}{( x^{2} -9)*(x+1)}= \frac{(x-3)*(x+3)*(x-1)}{(x-3)*(x+3)*(x+1)}$$= \frac{x-1}{x+1}$