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

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

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

simplify

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

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

Solution steps

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

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

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

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

Apply the fraction rule:

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

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

\frac{56}{63}

9 x + 3

(4 i) (- 3 i)

\frac{1}{8} + \frac{1}{5}

(3 x - 1) (2 x^{2} - 7 x - 4)

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