Question

1,2,3,4 va rog cu rezolvarea completa

Answer 1

[tex]1. \frac{ (x+4)(x-4)}{(x+4)(x+1)} \\ 2. \frac{x^2+5x}{x^2+10x+25} = \frac{x(x+5)}{(x+5)^2} = \frac{x}{x+5} \\ 3. \frac{x}{x-2} + \frac{x}{x+2} = \frac{x(x+2)}{(x+2)(x-2)} + \frac{x(x-2)}{(x-2)(x+2)} = \frac{x^2+2x}{x^2-2^2} + \frac{x^2-2x}{x^2-2^2} = \frac{x^2+2x+x^2-2x}{x^2-4} \\ = \frac{2x^2}{x^2-4} \\ 4. \frac{x^2-36}{4a^2} * \frac{(-2a)^2}{(x+6)^2} = \frac{(x-6)(x+6)}{4a^2} * \frac{4a^2}{(x+6)^2} = \frac{x-6}{x+6} [/tex]

Answer 2

1) (x-4)/(x+1) amplificat cu (x+4) este:
(x-4)(x+4)/ (x+1)(x+4) = (x^2-16)/(x^2+4x+x+4) = (x^2-16)/(x^2+5x+4)

2) (x^2+5x)/(x^2+10x+25) = x(x+5)/(x+5)^2 = x/(x+5)

3) x/(x-2) + x/(x+2) = x(x+2)/(x-2)(x+2) + x(x-2)/(x+2)(x-2) =
= (x^2+2x+x^2-2x)/((x^2-4) = 2x^2/(x^2-4)

4) (x^2-36)/4a^2 x [-2a/(x+6)]^2 = (x+6)(x-6)/4a^2 x [4a^2/(x+6)^2] = 
= (x-6)/(x+6)