What is (1-9w^2)/(12w-4) ?

The solution to (1-9w^2)/(12w-4) is -(1+3w)/4

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simplify (1-9w^2)/(12w-4)

simplify

\frac{1 - 9 w ^{2}}{12 w - 4}

- \frac{1 + 3 w}{4}

Solution steps

\frac{1 - 9 w ^{2}}{12 w - 4}

Factor

1 - 9 w^{2} : (1 + 3 w) (1 - 3 w)

= \frac{( 1 + 3 w ) ( 1 - 3 w )}{12 w - 4}

Factor

12 w - 4 : 4 (3 w - 1)

= \frac{( 1 + 3 w ) ( 1 - 3 w )}{4 ( 3 w - 1 )}

(1 + 3 w) (1 - 3 w) = - (1 + 3 w) (3 w - 1)

= \frac{- ( 1 + 3 w ) ( 3 w - 1 )}{4 ( 3 w - 1 )}

Cancel the common factor:

3 w - 1

= \frac{- ( 1 + 3 w )}{4}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{1 + 3 w}{4}

1 - \frac{1}{2 + \frac{1}{\frac{x}{3} - 1}}

+ z^{2} + 6 z - 27

2 x + 34 x + 1

\frac{4}{6} + \frac{3}{5}

\frac{2}{5} \times \frac{7}{3}