What is (5+1/(x-2))(1-1/(5x-9)) ?

The solution to (5+1/(x-2))(1-1/(5x-9)) is 5

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simplify (5+1/(x-2))(1-1/(5x-9))

simplify

(5 + \frac{1}{x - 2}) (1 - \frac{1}{5 x - 9})

5

Solution steps

(5 + \frac{1}{x - 2}) (1 - \frac{1}{5 x - 9})

Join

5 + \frac{1}{x - 2} : \frac{5 x - 9}{x - 2}

= \frac{5 x - 9}{x - 2} (1 - \frac{1}{5 x - 9})

Apply the fraction rule:

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

= \frac{( 5 x - 9 ) ( 1 - \frac{1}{5 x - 9} )}{x - 2}

Simplify

(5 x - 9) (1 - \frac{1}{5 x - 9}) : 5 x - 10

= \frac{5 x - 10}{x - 2}

Factor

5 x - 10 : 5 (x - 2)

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

Cancel the common factor:

x - 2

= 5

(3 x^{2} + x + 1) + (2 x^{2} - 3 x - 5)

lo g_{\frac{3}{2}} (\frac{27}{8})

\frac{20}{30}

\frac{2}{3} \cdot (- 1)

2 x - 4 x