What is (1-1/(5x))(1-3/(5x)) ?

The solution to (1-1/(5x))(1-3/(5x)) is ((5x-1)(5x-3))/(25x^2)

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simplify (1-1/(5x))(1-3/(5x))

simplify

(1 - \frac{1}{5 x}) (1 - \frac{3}{5 x})

\frac{( 5 x - 1 ) ( 5 x - 3 )}{25 x ^{2}}

Solution steps

(1 - \frac{1}{5 x}) (1 - \frac{3}{5 x})

Join

1 - \frac{1}{5 x} : \frac{5 x - 1}{5 x}

= \frac{5 x - 1}{5 x} (1 - \frac{3}{5 x})

Apply the fraction rule:

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

= \frac{( 5 x - 1 ) ( 1 - \frac{3}{5 x} )}{5 x}

Simplify

(5 x - 1) (1 - \frac{3}{5 x}) : \frac{( 5 x - 1 ) ( 5 x - 3 )}{5 x}

= \frac{\frac{( 5 x - 1 ) ( 5 x - 3 )}{5 x}}{5 x}

Apply the fraction rule:

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

= \frac{( 5 x - 1 ) ( 5 x - 3 )}{5 x \cdot 5 x}

Simplify

5 x \cdot 5 x : 25 x^{2}

= \frac{( 5 x - 1 ) ( 5 x - 3 )}{25 x ^{2}}

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\frac{8 x - 5}{( 4 x - 7 ) ^{2}}

What is (1-1/(5x))(1-3/(5x)) ?
The solution to (1-1/(5x))(1-3/(5x)) is ((5x-1)(5x-3))/(25x^2)