Problem 23 - College Algebra

Question

Multiply or 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 \(\frac{7}{9}\).

Step 1: Rewrite the division as a multiplication

The division of two fractions can be rewritten as a multiplication by the reciprocal of the second fraction. Thus, the given expression \(\frac{x+1}{3} \div \frac{3x+3}{7}\) can be rewritten as \(\frac{x+1}{3} \cdot \frac{7}{3x+3}\).

Step 2: Simplify before multiplying

Simplify the equation if possible before multiplying. Here in \(\frac{7}{3x+3}\), the 3 can be factored out from the denominator to yield \(\frac{7}{3} \cdot \frac{1}{x+1}\). Simplifying, it results in \(\frac{x+1}{3} \cdot \frac{7}{3(x+1)}\). The factor \((x+1)\) in numerator and denominator can be cancelled out.

Step 3: Perform the multiplication

Now, we are left with \(\frac{1}{3} \cdot \frac{7}{3}\), which simplifies to \(\frac{7}{9}\).