Perform the indicated operation: (a + 3)/(a^2 - 9) / (4a + 12)/(5a - 15)?

Question

(a + 3)/(a^2 - 9) / (4a + 12)/(5a - 15)

Write the answer in lowest terms.

Thank you

Answer 1

(a + 3)/(a^2 - 9) / (4a + 12)/(5a - 15)

Since everything is being divided here...
All you have to do is switch the second fraction, i.e. reciprocate it, and then multiply...

(a + 3)/(a^2 - 9) * (5a-15) /(4a + 12)

NOw multiply...
(5a^2-45) / (4a^3+12a^2 - 36a -108)

NOw factor out a 5 from the numerator and a 4 from the denominator:
5/4 * (a^2-9) / (a^3 +3a^2 -9a - 36)
Both the numerator and denominator have a factor of a+3

5/4 * (a+3)(a-3) / (a+3) (a+3)(a-3)
So the remaining part is...
5/4(a+3)

That is the answer:

5/ (4a+12)

Answer 2

a+3/a-3 a+3 / 4(a+3),/ 5(a-3)

a+3/ (a-3)(a+3) * 5(a-3) / 4(a+3)

20(a+3)=20a +60

2 a-3 and a+3 cancel out