What is (6a)/(a^2-9)+a/(a+3) ?

The solution to (6a)/(a^2-9)+a/(a+3) is a/(a-3)

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simplify (6a)/(a^2-9)+a/(a+3)

simplify

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

\frac{a}{a - 3}

Solution steps

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

Least Common Multiplier of

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

Adjust Fractions based on the LCM

= \frac{6 a}{( a + 3 ) ( a - 3 )} + \frac{a ( a - 3 )}{( a + 3 ) ( a - 3 )}

Apply the fraction rule:

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

= \frac{6 a + a ( a - 3 )}{( a + 3 ) ( a - 3 )}

Simplify

6 a + a (a - 3) : a^{2} + 3 a

= \frac{a ^{2} + 3 a}{( a + 3 ) ( a - 3 )}

Cancel

\frac{a ^{2} + 3 a}{( a + 3 ) ( a - 3 )} : \frac{a}{a - 3}

= \frac{a}{a - 3}

\frac{x ^{2} + 4 x + 4}{x ^{2} + 7 x + 10}

\frac{x}{2} + 4

\frac{cot ( x ) \cdot sec ( x )}{csc ( x )}

\frac{csc ( x )}{cot ( x ) + tan ( x )}

\frac{14}{6}