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Chapter 0: Problem 24

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

Short Answer

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

Step by step solution

01

Rewrite the Division as a Multiplication

Rewrite the problem by changing the division into a multiplication and flipping the second fraction. \[\frac{x+5}{7} \div \frac{4x+20}{9} = \frac{x+5}{7} \cdot \frac{9}{4x+20}\]
02

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: \[\frac{x+5}{7} \cdot \frac{9}{4(x+5)}\]
03

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: \[\frac{9}{28}\]

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Most popular questions from this chapter

Simplify each expression. Assume that all variables represent positive numbers. $$ \left(\frac{x^{\frac{1}{2}} y^{-\frac{7}{4}}}{y^{-\frac{5}{4}}}\right)^{-4} $$

Evaluate each expression without using a calculator. $$8^{\frac{2}{3}}$$

Find all integers b so that the trinomial can be factored. $$ x^{2}+b x+15 $$

Evaluate each expression without using a calculator. $$125^{\frac{2}{3}}$$

Simplify using properties of exponents. $$\left(3 x^{\frac{2}{3}}\right)\left(4 x^{\frac{3}{4}}\right)$$
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