Question 7 Divide and, if possible, simplify: $$ \frac{2 a^{2}+2 a}{4 a^{2}-12 a} \div \frac{a^{2}-1}{6 a-18} $$ O A. $$ \frac{a+1}{3} $$ O B. $$ \frac{a-1}{3} $$ O C. $$ \frac{3}{a+1} $$ O D. $$ \frac{3}{a-1} $$

Question

UpStudy AI · Accepted Answer

Factor each expression first.

1. For the first fraction:
   $$
   \frac{2a^2+2a}{4a^2-12a}
   $$
   Factor the numerator:
   $$
   2a^2+2a = 2a(a+1)
   $$
   Factor the denominator:
   $$
   4a^2-12a = 4a(a-3)
   $$
   So the first fraction becomes:
   $$
   \frac{2a(a+1)}{4a(a-3)} = \frac{a+1}{2(a-3)}
   $$

2. For the second fraction:
   $$
   \frac{a^2-1}{6a-18}
   $$
   Factor the numerator (difference of squares):
   $$
   a^2-1 = (a-1)(a+1)
   $$
   Factor the denominator:
   $$
   6a-18 = 6(a-3)
   $$
   So the second fraction becomes:
   $$
   \frac{(a-1)(a+1)}{6(a-3)}
   $$

3. Divide the first fraction by the second fraction:
   $$
   \frac{a+1}{2(a-3)} \div \frac{(a-1)(a+1)}{6(a-3)} = \frac{a+1}{2(a-3)} \times \frac{6(a-3)}{(a-1)(a+1)}
   $$
   Cancel the common factors $$(a+1)$$ and $$(a-3)$$:
   $$
   = \frac{6}{2(a-1)} = \frac{3}{a-1}
   $$

The simplified result is:
$$
\frac{3}{a-1}
$$

Thus, the correct answer is option D.
The simplified result is $$ \frac{3}{a-1} $$, so the correct answer is option D.

Question 7
Divide and, if possible, simplify:
O A.
O B.
O C.
O D.

Upstudy AI Solution

Answer

Solution

Beyond the Answer

Related Questions

Latest Algebra Questions

Question 7 Divide and, if possible, simplify: O A. O B. O C. O D.