Question

Resolva as expressões, simplificando o resultado sempre que possivel.


A) 2/a + a/3


B) 2/x + 2x/3 - 5/2x


C) -5a/b + 5a/2b - 5a/3b


D) 2y/y²-9 - 1/y-3 + 1/y+3


E) b/ab+b + a - 3a/a+1


F) 5/x-2 + -2/2x+4 + 2

Answer 1

$A)\\\\ \frac{2}{a} +\frac{a}{3} \\ \\ mmc=3a\\ \\ \frac{6+a^{2} }{3a}$

$B)\\ \\ \frac{2}{x} +\frac{2x}{3} -\frac{5}{2x} \\ \\ mmc=6x\\ \\ \frac{12+4x^{2}-15}{6x} =\frac{4x^{2}-3}{6x} =\frac{4x^{2}}{6x} -\frac{3}{6x} =~~~~\frac{2x}{3} -\frac{1}{2x}$

$C)\\ \\ \frac{-5a}{b} +\frac{5a}{2b} -\frac{5a}{3b} \\ \\ mmc=6b\\ \\ \frac{-30a+15a-10a}{6b} =\frac{-25a}{6b}$

$D)\\ \\ \frac{2y}{y^{2}-9} -\frac{1}{y-3} +\frac{1}{y+3} \\ \\ y^{2} -9=(y+3)(y-3)~, substitua:\\ \\ \frac{2y}{(y+3)(y-3)} -\frac{1}{y-3} +\frac{1}{y+3} \\ \\ mmc=(y+3)(y-3)\\ \\ \frac{2y-y+3+y-3}{(y+3)(y-3)} \\ \\ \frac{2y}{(y+3)(y-3)} =\frac{2y}{y^{2}+9}$

$E)\\ \\ \frac{b}{ab+b} +a-\frac{3a}{a+1} \\ \\ \frac{b}{b(a+1)} +a-\frac{3a}{a+1} \\ \\ \frac{1}{a+1} +a-\frac{3a}{a+1} \\ \\ mmc=a+1\\ \\ \frac{1+a(a+1)-3a}{a+1} \\ \\ \frac{1+a^{2}+a-3a}{a+1} \\ \\ \frac{a^{2}-2a+1}{a+1}$

$F)\\ \\ \frac{5}{x-2} +\frac{-2}{2x+4} +2\\ \\ 2x+4=2(x+2)~,substitua\\ \\ \frac{5}{x-2} +\frac{-2}{2(x+2)} +2=\frac{5}{x-2} -\frac{1}{x+2} +2\\ \\ mmc=(x+2)(x-2)\\ \\ \frac{5x+10-x-2+2(x^{2}+4)}{(x+2)(x-2)} \\ \\ \frac{5x+10-x-2+2x^{2}+8 }{x^{2}-4} \\ \\ \frac{2x^{2}+4x+16}{x^{2}+4}$