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Chapter 0: Problem 23

Multiply or divide as indicated. $$\frac{x+1}{3} \div \frac{3 x+3}{7}$$

Short Answer

Expert verified
The simplified result of the given expression is \( \frac{7}{9} \).

Step by step solution

01

Write the division as multiplication

The division of rational expressions can be written as a multiplication by swapping the divisor with its reciprocal. Hence the problem \( \frac{x+1}{3} \div \frac{3 x+3}{7} \) becomes \( \frac{x+1}{3} \times \frac{7}{3x+3} \).
02

Simplify the expression

Before multiplying, look for common factors that can be cancelled in both the numerators and denominators. Factor out like terms for simplification. \(3x+3\) can be rewritten as \(3(x+1)\). So the multiplication becomes \( \frac{x+1}{3} \times \frac{7}{3(x+1)} \). Notice here, \(x+1\) is a common term that can be cancelled.
03

Cancel the common factors

When you cancel the \(x+1\) in both the numerator and the denominator, you have \( \frac{1}{3} \times \frac{7}{3} \).
04

Perform multiplication

Multiply the remaining numerators together to get the numerator of the answer and do the same for the denominators. \( \frac{1}{3} \times \frac{7}{3} = \frac{1 \times 7}{3 \times 3} = \frac{7}{9} \).

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