2 a)
(x-3)*(x-7)=x²-7x-3x+21=x²-10x+21
b)
E(x)=[tex](\frac{2x^{2} -7x-17}{(x-3)(x-7)}-\frac{x+1}{x-7} ):\frac{1}{x^{2} -9}[/tex]=[tex]\frac{2x^{2} -7x-17-(x+1)(x-3)}{(x-3)(x-7)}:\frac{1}{x^{2} -9}[/tex]=[tex]\frac{2x^{2} -7x-17-x^{2}+2x+3 }{(x-3)(x-7)}:\frac{1}{x^{2} -9}[/tex]=[tex]\frac{x^{2} -5x-14}{(x-3)(x-7)}*\frac{x^{2} -9}{1}[/tex]=[tex]\frac{x^{2} -5x-14}{(x-3)(x-7)}*\frac{(x-3)(x+3)}{1}[/tex]
Ecuatia x²-5x-14 se poate descompune conform formulei ax²+bx+c=a(x-x1)(x-x2), unde x1,x2 sunt solutiile ecuatiei de gradul 2. Daca se egaleaza cu zero si se rezolva cu Δ se obtin solutiile 7 si -2. Atunci ecuatia devine:
[tex]\frac{(x-7)(x+2)}{(x-3)(x-7)}*\frac{(x-3)(x+3)}{1}[/tex]=(x+2)(x+3)
