What is (x+1)/(x^2+6x+9)+(x-4)/(x^2-9) ?

The solution to (x+1)/(x^2+6x+9)+(x-4)/(x^2-9) is (2x^2-3x-15)/((x+3)^2(x-3))

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simplify (x+1)/(x^2+6x+9)+(x-4)/(x^2-9)

simplify

\frac{x + 1}{x ^{2} + 6 x + 9} + \frac{x - 4}{x ^{2} - 9}

\frac{2 x ^{2} - 3 x - 15}{( x + 3 ) ^{2} ( x - 3 )}

Solution steps

\frac{x + 1}{x ^{2} + 6 x + 9} + \frac{x - 4}{x ^{2} - 9}

Least Common Multiplier of

x^{2} + 6 x + 9, x^{2} - 9 : (x + 3)^{2} (x - 3)

Adjust Fractions based on the LCM

= \frac{( x + 1 ) ( x - 3 )}{( x + 3 ) ^{2} ( x - 3 )} + \frac{( x - 4 ) ( x + 3 )}{( x + 3 ) ^{2} ( x - 3 )}

Apply the fraction rule:

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

= \frac{( x + 1 ) ( x - 3 ) + ( x - 4 ) ( x + 3 )}{( x + 3 ) ^{2} ( x - 3 )}

Simplify

(x + 1) (x - 3) + (x - 4) (x + 3) : 2 x^{2} - 3 x - 15

= \frac{2 x ^{2} - 3 x - 15}{( x + 3 ) ^{2} ( x - 3 )}

\frac{x ^{2} - 14 x + 45}{x ^{2} - 18 x + 81}

lo g_{10} (\frac{1}{10})

(3 x + 4 b) (3 x - 4 b)

1 0^{- 2.3}

\frac{2}{- 12}

What is (x+1)/(x^2+6x+9)+(x-4)/(x^2-9) ?
The solution to (x+1)/(x^2+6x+9)+(x-4)/(x^2-9) is (2x^2-3x-15)/((x+3)^2(x-3))