If x+\frac{1}{x}=\frac{5}{2}, then what is the value of the following? \frac{5x}{7x^2-3x+7}

Explanation

Divide the numerator and the denominator by x: \frac{5}{7x - 3 + \frac{7}{x}} = \frac{5}{7(x + \frac{1}{x}) - 3}. Substituting x + \frac{1}{x} = \frac{5}{2} gives \frac{5}{7(\frac{5}{2}) - 3} = \frac{5}{\frac{35}{2} - 3} = \frac{5}{\frac{29}{2}} = \frac{10}{29}.

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