What is ({(x-1/2)^2-21/4 })/((x-1-2/x)) ?

The solution to ({(x-1/2)^2-21/4 })/((x-1-2/x)) is ((x^2-x-5)x)/(x^2-x-2)

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simplify ({(x-1/2)^2-21/4 })/((x-1-2/x))

simplify

\frac{{ ( x - \frac{1}{2} ) ^{2} - \frac{21}{4} }}{( x - 1 - \frac{2}{x} )}

\frac{( x ^{2} - x - 5 ) x}{x ^{2} - x - 2}

Solution steps

\frac{( x - \frac{1}{2} ) ^{2} - \frac{21}{4}}{x - 1 - \frac{2}{x}}

Simplify

(x - \frac{1}{2})^{2} - \frac{21}{4} : x^{2} - x - 5

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

Join

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

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

Apply the fraction rule:

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

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

\frac{- 9 - 3 x ( - 3 ) + [ - 3 + 11 x ( - 3 ) ]}{2}

12 x^{5} y^{3} - 4 x^{2} y^{2}

- 273.1 5^{0} c

- 5 y - 5 y^{2}

(x)^{\frac{1}{2}} \cdot x^{2}

What is ({(x-1/2)^2-21/4 })/((x-1-2/x)) ?
The solution to ({(x-1/2)^2-21/4 })/((x-1-2/x)) is ((x^2-x-5)x)/(x^2-x-2)