Explicație pas cu pas:
a)
[tex] {x}^{2} + 4x + 3 = {x}^{2} + 3x + x + 3 = x(x + 3) + (x + 3) = (x + 3)(x + 1)[/tex]
b)
[tex]E(x) = ( \frac{4}{x - 1} + \frac{13 - 5x}{1 - {x}^{2} } - \frac{2x + 6}{ {x}^{2} + 4x + 3} ) \div \frac{1}{x + 1} = ( \frac{4}{x - 1} + \frac{5x - 13}{(x - 1)(x + 1)} - \frac{2(x + 3)}{(x + 1)(x + 3)} ) \times (x + 1) = ( \frac{4}{x - 1} + \frac{5x - 13}{(x - 1)(x + 1)} - \frac{2}{(x + 1)} ) \times (x + 1) = ( \frac{4(x + 1)}{(x - 1)(x + 1)} + \frac{5x - 13}{(x - 1)(x + 1)} - \frac{2(x - 1)}{(x + 1)(x - 1)} ) \times (x + 1) = \frac{4(x + 1) + (5x - 13) - 2(x - 1)}{(x + 1)(x - 1)} \times (x + 1) = \frac{4x + 4 + 5x - 13 - 2x + 2}{x - 1} = \frac{7x - 7}{x - 1} = \frac{7(x - 1)}{x - 1} = 7[/tex]
