Question

Alguem me ajude!!!

POR FAVOR!!!
                         SOCORROOOOO!!!       26 PONTOS

Answer 1

a)

$\frac{x}{x^2-4} - \frac{5}{x+2} =$

$\frac{x}{(x+2)(x-2)} - \frac{5}{x+2} =$

mmc=(x+2)(x-2)

$\frac{x-5(x-2)}{(x+2)(x-2)} = \frac{x-5x+10}{(x+2)(x-2)} = \frac{-4x+10}{x^2-4}$

b)

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

mmc=(a+b)(a-b)

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

c)

$\frac{x}{x+y} + \frac{y}{x+y} =$

mmc=x+y

$\frac{x+y}{x+y} =1$

d)

$\frac{1+x}{1-x} - \frac{1-x}{1+x} =$

mmc=(1+x)(1-x)

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

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

cancela =x²  com  -x²  e 1 com -1

$\frac{4x}{1-x^2}$

e)

$\frac{a}{a-b} - \frac{b}{b+a} =$

mmc=(a-b)(a+b)

$\frac{a(b+a)-b(a-b)}{(a+b)(a-b)} = \frac{ab+a^2-ab+b^2}{(a+b)(a-b)} =$

cancela  ab com -ab

$\frac{a^2+b^2}{a^2-b^2}$

f)

$\frac{a^2-4}{a^2+2a} + \frac{1}{a} = \frac{a^2-4}{a(a+2)} + \frac{1}{a} =$

mmc=a(a+2)

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

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