What is (1-1/x)(1-2/(x+2))(1-3/(x+5))(1-4/(x+9)) ?

The solution to (1-1/x)(1-2/(x+2))(1-3/(x+5))(1-4/(x+9)) is (x-1)/(x+9)

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simplify (1-1/x)(1-2/(x+2))(1-3/(x+5))(1-4/(x+9))

simplify

(1 - \frac{1}{x}) (1 - \frac{2}{x + 2}) (1 - \frac{3}{x + 5}) (1 - \frac{4}{x + 9})

\frac{x - 1}{x + 9}

Solution steps

(1 - \frac{1}{x}) (1 - \frac{2}{x + 2}) (1 - \frac{3}{x + 5}) (1 - \frac{4}{x + 9})

Join

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

= \frac{x - 1}{x} (1 - \frac{2}{x + 2}) (1 - \frac{3}{x + 5}) (1 - \frac{4}{x + 9})

Apply the fraction rule:

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

= \frac{( x - 1 ) ( 1 - \frac{2}{x + 2} ) ( 1 - \frac{3}{x + 5} ) ( 1 - \frac{4}{x + 9} )}{x}

Simplify

(x - 1) (1 - \frac{2}{x + 2}) (1 - \frac{3}{x + 5}) (1 - \frac{4}{x + 9}) : \frac{( x - 1 ) x}{x + 9}

= \frac{\frac{( x - 1 ) x}{x + 9}}{x}

Apply the fraction rule:

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

= \frac{( x - 1 ) x}{( x + 9 ) x}

Cancel the common factor:

x

= \frac{x - 1}{x + 9}

sin (2 (n + 1))

- 6.3 (A + B sin (D x) + C cos (D x))

\frac{z}{( z - 1 ) ( z + 4 )}

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

(x^{3} - 2 x^{2} + \frac{1}{2})^{3}

What is (1-1/x)(1-2/(x+2))(1-3/(x+5))(1-4/(x+9)) ?
The solution to (1-1/x)(1-2/(x+2))(1-3/(x+5))(1-4/(x+9)) is (x-1)/(x+9)