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Chapter 7: Problem 41

Divide as indicated. $$\frac{7}{x-5} \div \frac{28}{3 x-15}$$

Short Answer

Expert verified
\(\frac{3}{4}\)

Step by step solution

01

Rewrite the division as a multiplication

Rewrite \(\frac{7}{x-5} \div \frac{28}{3x-15}\) as \(\frac{7}{x-5} \times \frac{3x-15}{28}\)
02

Simplify

Simplify \(\frac{7}{x-5} \times \frac{3x-15}{28}\) to \(\frac{7}{x-5} \times \frac{3(x-5)}{28}\)
03

Cancel common factors

Cancel out the common factors of \(x-5\) in the numerator and the denominator to get \(\frac{7}{1} \times \frac{3}{28}\)
04

Multiply the fractions

Multiply \(\frac{7}{1} \times \frac{3}{28}\) to get \(\frac{21}{28}\)
05

Simplify the fraction

Simplify the fraction \(\frac{21}{28}\) to \(\frac{3}{4}\) by dividing the numerator and the denominator by their greatest common divisor, 7

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Most popular questions from this chapter

perform the indicated operations. Simplify the result, if possible. $$\left(\frac{3 x-1}{x^{2}+5 x-6}-\frac{2 x-7}{x^{2}+5 x-6}\right) \div \frac{x+2}{x^{2}-1}$$

denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{2 x-y}{x-y}+\frac{x-2 y}{y-x}$$

Add or subtract as indicated. Simplify the result, if possible. $$\frac{x+3}{2}+\frac{x+5}{4}$$

determine whether each statement 鈥渕akes sense鈥� or 鈥渄oes not make sense鈥� and explain your reasoning. I added \(\frac{5}{x-7}\) and \(\frac{3}{7-x}\) by first multiplying the second rational expression by \(-1\)

use the GRAPH or TABLE feature of a graphing utility to determine if the subtraction has been performed correctly. If the answer is wrong, correct it and then verify your correction using the graphing utility. $$\frac{3 x+6}{2}-\frac{x}{2}=x+3$$
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