Problem 38
Question
Divide as indicated. $$\frac{9}{x} \div \frac{3}{4 x}$$
Step-by-Step Solution
Verified Answer
The solution to \( \frac{9}{x} \div \frac{3}{4x} \) is 12.
1Step 1 Title: Find the Reciprocal
Swap the numerator and denominator in the divisor, \( \frac{3}{4x} \) which results in \( \frac{4x}{3} \). This is known as finding the reciprocal.
2Step 2 Title: Multiply the fractions
After changing the operation to multiplication, we need to multiply the two fractions. So, multiply \( \frac{9}{x} \) and \( \frac{4x}{3} \). When multiplying fractions, we simply multiply the numerators together and the denominators together. This results in \( \frac{9 * 4x}{x * 3} \) = \( \frac{36x}{3x} \).
3Step 3 Title: Simplify the Result
We simplify the result by canceling out the common factors. In this case, x in the numerator and denominator can be cancelled out. Therefore, \( \frac{36x}{3x} \) simplifies to \( \frac{36}{3} = 12 \).
Other exercises in this chapter
Problem 38
Simplify each rational expression. If the rational expression cannot be simplified, so state. $$\frac{x+2}{x^{2}-x-6}$$
View solution Problem 38
Simplify complex rational expression by the method of your choice. \(\frac{\frac{2}{x^{3} y}+\frac{5}{x y^{4}}}{\frac{5}{x^{3} y}-\frac{3}{x y}}\)
View solution Problem 38
Solve each rational equation. $$\frac{1}{x-1}+\frac{2}{x}=\frac{x}{x-1}$$
View solution Problem 39
denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{4}{x-3}+\frac{2}{3-x}$$
View solution