Problem 24 - College Algebra

Question

Multiply or divide as indicated. $$\frac{x+5}{7} \div \frac{4 x+20}{9}$$

Step-by-Step Solution

Answer

The simplified form of the expression is \(\frac{9}{28}\)

Step 1: Rewrite the Division as a Multiplication

Rewrite the problem by changing the division into a multiplication and flipping the second fraction. \[\frac{x+5}{7} \div \frac{4x+20}{9} = \frac{x+5}{7} \cdot \frac{9}{4x+20}\]

Step 2: Simplify the Expression

We can simplify the expression by factoring out the common factors. \(4x + 20\) can be written as \(4(x + 5)\). After simplifying the expression looks like this: \[\frac{x+5}{7} \cdot \frac{9}{4(x+5)}\]

Step 3: Cancel out the common terms

In this step, the term \((x+5)\) in the numerator and the denominator cancel out each other. The simplified form is: \[\frac{9}{28}\]