Question

Efetue as operações com fraçoes algébricas:

Answer 1

Explicação passo-a-passo:

$a)\\ mmc(a+b)(a-b)\\ \\{2a(a-b)+(b-a)(a+b)\over(a+b)(a-b)}=\\ \\ {2a^2-2ab+ab+b^2-a^2-ab\over(a+b)(a-b)}=\\ \\ {2a^2-a^2-2ab+ab-ab+b^2\over(a+b)(a-b)}=\\ \\ {a^2-2ab+b^2\over(a+b)(a-b)}=~~\\ \\ ~fatorando~~e ~~cancelando\\ \\ {(a-b)^2\over(a+b)(a-b)}={(a-b)\over (a+b)$

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$b)\\ {a^2+a\over(a+3)(a-3)}+{2\over a-3}+{1\over a+3}=\\ \\ mmc(a+3)(a-3)\\ \\ {a^2+a+2(a+3)+1(a-3)\over(a+3)(a-3)}=\\ \\ {a^2+a+2a+6+a-3\over(a+3)(a-3)}=\\ \\ {a^2+4a+3\over(a+3)(a-3)}=\\ \\ fatoranndo~~e~~cancelando\\ \\ {(a+1)(a+3)\over(a+3)(a-3)}={a+1\over a-3}$

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$c)\\ mmc=xyz\\ \\ {z(x-y)+x(y-z)+y(z-x)\over xyz}=\\ \\ {xz-yz+xy-xz+yz-xy\over xyz}=\\ \\ cancelando\\ \\ {\not xz-\not xz-\not yz+\not yz+\not xy-\not xy\over xyz}={0\over xyz}=0$