Question

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Answer 1

Resposta e explicação passo-a-passo:

a)

$\frac{a +1}{a^{2} +2a+1} \\\\= \frac{a+1}{(a+1)^{2}} \\\\= \frac{1}{a+1}$

b)

$\frac{x^{2} +6x+ 9}{2x +6} \\\\= \frac{(x+3)^{2}}{2(x+3)} \\\\= \frac{x+3}{2}$

c)

$\frac{(x+y)^{2}}{x^{2}- y^{2}} \\\\= \frac{(x+y)^{2}}{(x+y)(x-y)} \\\\= \frac{x+y}{x-y}$

d)

$\frac{15x^{2} + 5x}{5x} \\\\= \frac{5x(3x+1)}{5x} \\\\= 3x + 1$

e)

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

f)

$\frac{4x^{2} - y^2}{2x - y}\\\\= \frac{(2x + y)(2x-y)}{2x-y}\\\\= 2x +y$

Espero ter ajudado :)