What is ((30z))/((9z^2-1))+2/((3z-1))-5/((3z+1)) ?

The solution to ((30z))/((9z^2-1))+2/((3z-1))-5/((3z+1)) is 7/(3z-1)

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simplify ((30z))/((9z^2-1))+2/((3z-1))-5/((3z+1))

simplify

\frac{( 30 z )}{( 9 z ^{2} - 1 )} + \frac{2}{( 3 z - 1 )} - \frac{5}{( 3 z + 1 )}

\frac{7}{3 z - 1}

Solution steps

\frac{30 z}{9 z ^{2} - 1} + \frac{2}{3 z - 1} - \frac{5}{3 z + 1}

Least Common Multiplier of

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

Adjust Fractions based on the LCM

= \frac{30 z}{( 3 z + 1 ) ( 3 z - 1 )} + \frac{2 ( 3 z + 1 )}{( 3 z + 1 ) ( 3 z - 1 )} - \frac{5 ( 3 z - 1 )}{( 3 z + 1 ) ( 3 z - 1 )}

Apply the fraction rule:

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

= \frac{30 z + 2 ( 3 z + 1 ) - 5 ( 3 z - 1 )}{( 3 z + 1 ) ( 3 z - 1 )}

Simplify

30 z + 2 (3 z + 1) - 5 (3 z - 1) : 21 z + 7

= \frac{21 z + 7}{( 3 z + 1 ) ( 3 z - 1 )}

Cancel

\frac{21 z + 7}{( 3 z + 1 ) ( 3 z - 1 )} : \frac{7}{3 z - 1}

= \frac{7}{3 z - 1}

(x + 2 x^{2})^{6}

\frac{4}{a} - \frac{3}{b}

14 - 3 x^{2} - 5 7 x

343 x^{3} + 125 y^{3}

32 u^{2} v - 50 v

What is ((30z))/((9z^2-1))+2/((3z-1))-5/((3z+1)) ?
The solution to ((30z))/((9z^2-1))+2/((3z-1))-5/((3z+1)) is 7/(3z-1)