Question

Qual o valor numérico de T na expressão T=\frac{1}{\frac{1}{x}+\frac{1}{y}} onde x = 2 e y = 3.

Answer 1

Olá.

$\mathsf{T=\dfrac{1}{\dfrac{1}{x}+\dfrac{1}{y}}}\\\\\\\\\left\{\begin{array}{c}\mathsf{x=2}\\\mathsf{y=3}\end{array}\right\\\\\\ \mathsf{T=\dfrac{1}{\dfrac{1}{2}+\dfrac{1}{3}}=\dfrac{1}{\dfrac{1\cdot3+1\cdot2}{6}}=\dfrac{1}{\dfrac{3+2}{6}}=\dfrac{1}{\dfrac{5}{6}}}\\\\\\\textsf{Usando~propriedades~de~fra\c{c}\~ao...}\\\\\mathsf{T=\dfrac{1}{\dfrac{5}{6}}=\dfrac{1}{1}\cdot\dfrac{6}{5}=\boxed{\mathsf{\dfrac{6}{5}}}}$

$\boxed{\boxed{\mathsf{T=\dfrac{6}{5}}}}$

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Bons estudos.