What is (6+1/x)/(7-1/x) ?

The solution to (6+1/x)/(7-1/x) is (6x+1)/(7x-1)

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simplify (6+1/x)/(7-1/x)

simplify

\frac{6 + \frac{1}{x}}{7 - \frac{1}{x}}

\frac{6 x + 1}{7 x - 1}

Solution steps

\frac{6 + \frac{1}{x}}{7 - \frac{1}{x}}

Join

6 + \frac{1}{x} : \frac{6 x + 1}{x}

= \frac{\frac{6 x + 1}{x}}{7 - \frac{1}{x}}

Join

7 - \frac{1}{x} : \frac{7 x - 1}{x}

= \frac{\frac{6 x + 1}{x}}{\frac{7 x - 1}{x}}

Apply the fraction rule:

\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a \cdot d}{b \cdot c}

= \frac{( 6 x + 1 ) x}{x ( 7 x - 1 )}

Cancel the common factor:

x

= \frac{6 x + 1}{7 x - 1}

4 \times (- \frac{1}{4})

4 x^{2} \times x

6 x^{2} - x - 35

(\frac{1}{36})^{\frac{5}{2}}

- 1.125 + \frac{24}{20}