What is (x-5+6x^{-1})/(1-2x^{-1)} ?

The solution to (x-5+6x^{-1})/(1-2x^{-1)} is x-3

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simplify (x-5+6x^{-1})/(1-2x^{-1)}

simplify

\frac{x - 5 + 6 x ^{- 1}}{1 - 2 x ^{- 1}}

x - 3

Solution steps

\frac{x - 5 + 6 x ^{- 1}}{1 - 2 x ^{- 1}}

Simplify

x - 5 + 6 x^{- 1} : \frac{x ^{2} - 5 x + 6}{x}

= \frac{\frac{x ^{2} - 5 x + 6}{x}}{1 - 2 x ^{- 1}}

Simplify

1 - 2 x^{- 1} : \frac{x - 2}{x}

= \frac{\frac{x ^{2} - 5 x + 6}{x}}{\frac{x - 2}{x}}

Apply the fraction rule:

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

= \frac{( x ^{2} - 5 x + 6 ) x}{x ( x - 2 )}

Cancel

\frac{( x ^{2} - 5 x + 6 ) x}{x ( x - 2 )} : x - 3

= x - 3

(a + ab)^{2}

2 sin (x) sin (x)

- 3 i \cdot (- 3) i

\frac{50}{12}

- 16 x - (5 x + 7 (- 3 x + 2))

What is (x-5+6x^{-1})/(1-2x^{-1)} ?
The solution to (x-5+6x^{-1})/(1-2x^{-1)} is x-3