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

Step by step solution

01

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 \(\frac{x+1}{3} \cdot \frac{7}{3x+3}\).
02

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.
03

Perform the multiplication

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

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