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

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

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simplify (ab)/(9a^2-b^2)+a/(3a+b)

simplify

\frac{ab}{9 a ^{2} - b ^{2}} + \frac{a}{3 a + b}

\frac{3 a ^{2}}{9 a ^{2} - b ^{2}}

Solution steps

\frac{ab}{9 a ^{2} - b ^{2}} + \frac{a}{3 a + b}

Least Common Multiplier of

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

Adjust Fractions based on the LCM

= \frac{ab ( 3 a + b )}{( 3 a + b ) ( 9 a ^{2} - b ^{2} )} + \frac{a ( 9 a ^{2} - b ^{2} )}{( 3 a + b ) ( 9 a ^{2} - b ^{2} )}

Apply the fraction rule:

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

= \frac{ab ( 3 a + b ) + a ( 9 a ^{2} - b ^{2} )}{( 3 a + b ) ( 9 a ^{2} - b ^{2} )}

Simplify

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

= \frac{9 a ^{3} + 3 a ^{2} b}{( 3 a + b ) ( 9 a ^{2} - b ^{2} )}

Cancel

\frac{9 a ^{3} + 3 a ^{2} b}{( 3 a + b ) ( 9 a ^{2} - b ^{2} )} : \frac{3 a ^{2}}{9 a ^{2} - b ^{2}}

= \frac{3 a ^{2}}{9 a ^{2} - b ^{2}}

\frac{4}{- 3}

(p + 5 q)^{2}

9 x^{4}

7 + 4 t + 5 (11 - 3 t)

(2 x + 3) (x - 1)

What is (ab)/(9a^2-b^2)+a/(3a+b) ?
The solution to (ab)/(9a^2-b^2)+a/(3a+b) is (3a^2)/(9a^2-b^2)