Problem 39 - Introductory Algebra for College Students

Question

Divide as indicated. $$\frac{x+1}{3} \div \frac{3 x+3}{7}$$

Step-by-Step Solution

Answer

The result of \(\frac{x+1}{3} \div \frac{3x+3}{7}\) is \(\frac{7x+7}{9x+9}\).

Step 1: Identify Dividend and Divisor

The problem provided is in the form \(\frac{a}{b} \div \frac{c}{d}\) where \(\frac{a}{b}\) is the dividend and \(\frac{c}{d}\) is the divisor. For our problem, \(\frac{x+1}{3}\) is the dividend and \(\frac{3x+3}{7}\) is the divisor.

Step 2: Calculate Reciprocal of Divisor

The reciprocal of a fraction is obtained by swapping the numerator and the denominator. Therefore, the reciprocal of our divisor \(\frac{3x+3}{7}\) is \(\frac{7}{3x+3}\).

Step 3: Multiply Dividend by Reciprocal of Divisor

Now, divide the first fraction by the second fraction which is equivalent to multiplication with the reciprocal of the divisor fraction: \(\frac{x+1}{3} \times \frac{7}{3x+3}\).

Step 4: Simplify the Multiplication of the Fractions

The multiplication operation gives us \(\frac{7(x+1)}{9x+9}\), which simplifies to \(\frac{7x+7}{9x+9}\).