What is ((3a-1/((3a))))/((3a-2+1/((3a)))) ?

The solution to ((3a-1/((3a))))/((3a-2+1/((3a)))) is (3a+1)/(3a-1)

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simplify ((3a-1/((3a))))/((3a-2+1/((3a))))

simplify

\frac{( 3 a - \frac{1}{( 3 a )} )}{( 3 a - 2 + \frac{1}{( 3 a )} )}

\frac{3 a + 1}{3 a - 1}

Solution steps

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

Join

3 a - \frac{1}{3 a} : \frac{9 a ^{2} - 1}{3 a}

= \frac{\frac{9 a ^{2} - 1}{3 a}}{3 a - 2 + \frac{1}{3 a}}

Join

3 a - 2 + \frac{1}{3 a} : \frac{9 a ^{2} - 6 a + 1}{3 a}

= \frac{\frac{9 a ^{2} - 1}{3 a}}{\frac{9 a ^{2} - 6 a + 1}{3 a}}

Apply the fraction rule:

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

= \frac{( 9 a ^{2} - 1 ) \cdot 3 a}{3 a ( 9 a ^{2} - 6 a + 1 )}

Cancel

\frac{( 9 a ^{2} - 1 ) \cdot 3 a}{3 a ( 9 a ^{2} - 6 a + 1 )} : \frac{3 a + 1}{3 a - 1}

= \frac{3 a + 1}{3 a - 1}

t^{7}

81 w^{2} z - 64 x^{2} z

\frac{14 a ^{2}}{21 a}

6 x y - 9 x^{2} - y^{2}

55 x^{2} - 3582 x^{2}

What is ((3a-1/((3a))))/((3a-2+1/((3a)))) ?
The solution to ((3a-1/((3a))))/((3a-2+1/((3a)))) is (3a+1)/(3a-1)