Question

Resolva as seguintes frações algébricas : a) 1/(x-1/x)+1
b) 4x+3/3x + 6/x² - 1/x
c) 1/x³ + 12/x² - 3/x

Answer 1

$\mathrm{\mathbf{a)}\ \dfrac{1}{\dfrac{x-1}{x}+1}=\dfrac{1}{\dfrac{1-x}{x}+\dfrac{x}{x}}=\dfrac{1}{\dfrac{1}{x}}=1.\dfrac{x}{1}=\boxed{\mathbf{x}}}$

$\mathrm{\mathbf{b)}\ \dfrac{4x+3}{3x}+\dfrac{6}{x^2}-\dfrac{1}{x}=\dfrac{4x+3}{3x}-\dfrac{3}{3x}+\dfrac{6}{x^2}=}\\\\ \mathrm{=\dfrac{4x}{3x}+\dfrac{6}{x^2}=\dfrac{4}{3}+\dfrac{6}{x^2}=\dfrac{4x^2+3.6}{3x^2}=\boxed{\mathbf{\dfrac{4x^2+18}{3x^2}}}}$

$\mathrm{\mathbf{c)}\ \dfrac{1}{x^3}+\dfrac{12}{x^2}-\dfrac{3}{x}=\dfrac{1.x^2.x+13.x^3.x-3.x^3.x^2}{x^3.x^2.x}=}\\\\ \mathrm{=\dfrac{x^3+13x^4-3x^5}{x^6}=\dfrac{x^3(1+13x-3x^2)}{x^3.x^3}=\boxed{\mathbf{\dfrac{-3x^2+13x+1}{x^3}}}}$