Problem 3
Question
Simplify the expression. $$\frac{3 x}{8 x^{2}} \cdot \frac{4 x^{3}}{3 x^{4}}$$
Step-by-Step Solution
Verified Answer
The simplified form of the given expression is \( \frac{1}{2x}\).
1Step 1: Simplify Numerators and Denominators
Divide both the numerator and denominator by their common factors. For this, \(\frac{3x}{8x^{2}} \cdot \(\frac{4x^{3}}{3x^{4}} = \frac{3}{8} \cdot \frac{x}{x^{2}} \cdot \frac{4}{3} \cdot \frac{x^{3}}{x^{4}}\).
2Step 2: Simplify Fractions
We find that the fractions \(\frac{3}{8} \cdot \frac{4}{3}\) and \( \frac{x}{x^{2}} \cdot \frac{x^{3}}{x^{4}}\) are independent of each other and can be simplified separately to \( \frac{1}{2}\) and \( \frac{1}{x}\) respectively.
3Step 3: Multiply Simplified Fractions
Multiplying these fractions produces the final result, which is \( \frac{1}{2x}\).
Other exercises in this chapter
Problem 3
Find the least common denominator. \(\frac{1}{x}, \frac{x}{3}, \frac{2}{3 x}\)
View solution Problem 3
Solve the proportion. Check your solution. $$ \frac{72}{96}=\frac{x}{4} $$
View solution Problem 3
Define the simplest form of a rational expression. Give an example of a rational expression in simplest form.
View solution Problem 4
Add. Simplify your answer. $$ \frac{x}{x^{2}-9}+\frac{3 x+1}{x^{2}-9} $$
View solution