Find the value of t such that the expression \(\frac{1}{t}\) + \(\frac{4}{3}\) - \(\frac{5}{6t}\) +...

Find the value of t such that the expression \(\frac{1}{t}\) + \(\frac{4}{3}\) - \(\frac{5}{6t}\) + 1 is equal to zero

A. \(\frac{1}{6}\)
B. \(\frac{1}{-14}\)
C. - \(\frac{3}{2}\)
D. \(\frac{7}{6}\)
E. \(\frac{2}{5}\)

\(\frac{1}{t}\) + \(\frac{4}{3}\) - \(\frac{5}{6t}\) + 1 = 0

collect like terms

\(\frac{4}{3}\) + 1 = \(\frac{5}{6t}\) - \(\frac{1}{t}\)

\(\frac{4 + 3}{3}\) = \(\frac{-1}{6t}\)

cross multiply

42t = - 3

t = \(\frac{-3}{42t}\)

t = \(\frac{-1}{14}\)

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