What is (a-1)/(a^2+5a+6)+(a+2)/(a^2-9) ?

The solution to (a-1)/(a^2+5a+6)+(a+2)/(a^2-9) is (2a^2+7)/((a+2)(a+3)(a-3))

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simplify (a-1)/(a^2+5a+6)+(a+2)/(a^2-9)

simplify

\frac{a - 1}{a ^{2} + 5 a + 6} + \frac{a + 2}{a ^{2} - 9}

\frac{2 a ^{2} + 7}{( a + 2 ) ( a + 3 ) ( a - 3 )}

Solution steps

\frac{a - 1}{a ^{2} + 5 a + 6} + \frac{a + 2}{a ^{2} - 9}

Least Common Multiplier of

a^{2} + 5 a + 6, a^{2} - 9 : (a + 2) (a + 3) (a - 3)

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

(a - 1) (a - 3) + (a + 2)^{2} : 2 a^{2} + 7

= \frac{2 a ^{2} + 7}{( a + 2 ) ( a + 3 ) ( a - 3 )}

\frac{x ^{2}}{2} \cdot \frac{1}{x}

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

- 9 x (5 - 2 x)

(4 - 8 i) - (8 - 4 i)

cos (θ) csc (θ)

What is (a-1)/(a^2+5a+6)+(a+2)/(a^2-9) ?
The solution to (a-1)/(a^2+5a+6)+(a+2)/(a^2-9) is (2a^2+7)/((a+2)(a+3)(a-3))