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Which of the following is equivalent to 
((3+(3)/(a)))/(((3)/(a))) ?
Choose 1 answer:
(A) 
a+1
(B) 
a
(C) 2
(D) 
(1)/(2)

Which of the following is equivalent to (3+3a)(3a) \frac{\left(3+\frac{3}{a}\right)}{\left(\frac{3}{a}\right)} ?\newlineChoose 11 answer:\newline(A) a+1 a+1 \newline(B) a a \newline(C) 22\newline(D) 12 \frac{1}{2}

Full solution

Q. Which of the following is equivalent to (3+3a)(3a) \frac{\left(3+\frac{3}{a}\right)}{\left(\frac{3}{a}\right)} ?\newlineChoose 11 answer:\newline(A) a+1 a+1 \newline(B) a a \newline(C) 22\newline(D) 12 \frac{1}{2}
  1. Simplify fractions: Simplify the numerator and the denominator.\newlineThe expression given is 3+3a3a\frac{3+\frac{3}{a}}{\frac{3}{a}}. We can start by simplifying the numerator and the denominator separately.\newlineThe numerator is 3+3a3 + \frac{3}{a}, which can be written as a single fraction by finding a common denominator.\newlineThe denominator is 3a\frac{3}{a}, which is already a single fraction.
  2. Combine terms: Combine the terms in the numerator.\newlineTo combine 33 and 3a\frac{3}{a}, we need a common denominator, which is 'aa'. So we convert 33 to a fraction with the same denominator:\newline3=3aa3 = \frac{3a}{a}\newlineNow we can add the two fractions:\newline3aa+3a=3a+3a\frac{3a}{a} + \frac{3}{a} = \frac{3a + 3}{a}
  3. Rewrite expression: Rewrite the original expression with the simplified numerator.\newlineNow that we have the simplified numerator, we can rewrite the original expression as:\newline(3a+3)a÷3a\frac{(3a + 3)}{a} \div \frac{3}{a}
  4. Divide fractions: Divide the fractions.\newlineTo divide fractions, we multiply the first fraction by the reciprocal of the second fraction:\newline3a+3a×a3\frac{3a + 3}{a} \times \frac{a}{3}
  5. Simplify expression: Simplify the expression.\newlineWhen we multiply the fractions, we can cancel out the 'aa' in the numerator of the first fraction and the 'aa' in the denominator of the second fraction:\newline(3a+3)/3(3a + 3)/3
  6. Divide terms: Divide each term in the numerator by the denominator.\newlineNow we divide each term in the numerator by 33:\newline(3a/3)+(3/3)(3a/3) + (3/3)\newlineThis simplifies to:\newlinea+1a + 1

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