Answer:
The correct answer is (a + 3)³/5
Explanation:
Points to remember:
1). (a + b)(a - b) = a² - b²
2). If we want to divide two fractions, we need to multiply the reciprocal of divisor with dividend.
It is given that,
(a + 3)²/a-3 ÷ 5/(a²-9),
To find the division result
(a + 3)²/a-3 ÷ 5/(a² - 9)
Reciprocal of 5/(a² - 9) = (a² - 9)/5
(a + 3)²/a-3 ÷ 5/(a² - 9) = (a + 3)²/(a -3) * (a² - 9)/5
(a² - 9) = (a + 3)(a - 3) [ using identity]
(a + 3)²/(a -3) * (a² - 9)/5 = (a + 3)²/(a -3) * (a + 3)(a - 3) /5
= (a + 3)²(a + 3)(a - 3)/(a -3)5
= (a + 3)²(a + 3)/5 = (a + 3)³/5
Therefore the correct answer is (a + 3)³/5