What is (z-1/2)(z-1/3) ?

The solution to (z-1/2)(z-1/3) is ((2z-1)(3z-1))/6

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simplify (z-1/2)(z-1/3)

simplify

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

\frac{( 2 z - 1 ) ( 3 z - 1 )}{6}

Solution steps

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

Simplify

z - \frac{1}{2} : \frac{2 z - 1}{2}

= \frac{2 z - 1}{2} (z - \frac{1}{3})

Apply the fraction rule:

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

= \frac{( 2 z - 1 ) ( z - \frac{1}{3} )}{2}

Simplify

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

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

Apply the fraction rule:

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

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

Multiply the numbers:

3 \cdot 2 = 6

= \frac{( 2 z - 1 ) ( z \cdot 3 - 1 )}{6}

= \frac{( 2 z - 1 ) ( 3 z - 1 )}{6}

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