Add the fractions. If possible, simplify your answer. 7a2+6a+9+8a2−9=?

Step 1 We have given to add fractions. 7a2+6a+9+8a2−9 =a2+6a+9=a2+2⋅3a+32=(a+3)2 =a2−9=(a−3)(a+3) =7a2+6a+9+8a2−9=7(a+3)2+8(a+3)(a−3) =7(a−3)+8(a+3)(a+3)2(a−3) =7a−21+8a+24(a+3)2(a−3) =15a+3(a+3)2(a−3) =3(5a+1)(a+3)2(a−3) =7a2+6a+9+8a2=9=3(5a+1)(a+3)2(a−3) Step 2 Hence on adding fractions we get result equal to 3(5a+1)(a+3)2(a−3)

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Pre-Algebra
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sagnuhh

Answered question

2021-09-18

Add the fractions. If possible, simplify your answer.

\frac{7}{a^{2} + 6 a + 9} + \frac{8}{a^{2} - 9} = ?

Answer & Explanation

yagombyeR

Skilled2021-09-19Added 92 answers

Step 1
We have given to add fractions.

\frac{7}{a^{2} + 6 a + 9} + \frac{8}{a^{2} - 9}

= a^{2} + 6 a + 9 = a^{2} + 2 \cdot 3 a + 3^{2} = {(a + 3)}^{2}

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

= \frac{7}{a^{2} + 6 a + 9} + \frac{8}{a^{2} - 9} = \frac{7}{{(a + 3)}^{2}} + \frac{8}{(a + 3) (a - 3)}

= \frac{7 (a - 3) + 8 (a + 3)}{{(a + 3)}^{2} (a - 3)}

= \frac{7 a - 21 + 8 a + 24}{{(a + 3)}^{2} (a - 3)}

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

= \frac{3 (5 a + 1)}{{(a + 3)}^{2} (a - 3)}

= \frac{7}{a^{2} + 6 a + 9} + \frac{8}{a^{2} = 9} = \frac{3 (5 a + 1)}{{(a + 3)}^{2} (a - 3)}

Step 2
Hence on adding fractions we get result equal to

\frac{3 (5 a + 1)}{{(a + 3)}^{2} (a - 3)}

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