Question

Arătați că: .............​

Answer 1

Răspuns:

Explicație pas cu pas:

$E(x)=\displaystyle \frac{x^{2} -9}{x^{2}-4x+3 } +\frac{x+2}{x+1} -\frac{x^{2}+5x+2 }{x^{2} -1}$

$x^{2} -9=x^{2} -3^{2} =(x-3)(x+3)$

$x^{2} -4x+3=x^{2} -x-3x+3=x(x-1)-3(x-1)=(x-1)(x-3)$

$x^{2} -1=(x-1)(x+1)$

$E(x) = \displaystyle \frac{(x-3)(x+3)}{(x-1)(x-3)} +\frac{x+2}{x+1} -\frac{x^{2}+5x+2 }{(x-1)(x+1)}$

$E(x)=\displaystyle \frac{x+3}{x-1} +\frac{x+2}{x+1} -\frac{x^{2} +5x+2}{(x-1)(x+1)} \\ \\ numitorul comun este (x-1)(x+1)$

$E(x)=\displaystyle\frac{(x+3)(x+1)}{(x-1)(x+1)} +\frac{(x+2)(x-1)}{(x-1)(x+1)} -\frac{x^{2}+5x+2 }{(x-1)(x+1)}$

$E(x)=\displaystyle \frac{x^{2}+x+3x+3 }{(x-1)(x+1)} +\frac{x^{2}-x+2x-2 }{(x-1)(x+1)} -\frac{x^{2}+5x+2 }{(x-1)(x+1)}$

$E(x)=\displaystyle \frac{x^{2}+4x+3+x^{2} +x-2-x^{2} -5x-2 }{(x-1)(x+1)}$

$E(x)=\displaystyle \frac{x^{2} -1}{x^{2} -1} =1$

am folosit formula a²-b²=(a-b)(a+b)

ab±ac=a(b±c)