Questions: Divide. x/5 ÷ (x+4)/15 State the quotient in simplest form. x/5 ÷ (x+4)/15 = / Enter the numerator and denominator separately in the boxes above. If the denominator is 1, enter the number 1. Do not leave either box blank.

Divide. x/5 ÷ (x+4)/15
State the quotient in simplest form.

x/5 ÷ (x+4)/15 = /

Enter the numerator and denominator separately in the boxes above. If the denominator is 1, enter the number 1. Do not leave either box blank.

Transcript text: Divide. $\frac{x}{5} \div \frac{x+4}{15}$ State the quotient in simplest form. \[ \frac{x}{5} \div \frac{x+4}{15}=\frac{\square}{\square} \] Enter the numerator and denominator separately in the boxes above. If the denominator is 1 , enter the number 1 . Do not leave either box blank.

Solution

Solution Steps

Step 1: Rewrite the Division as Multiplication

To divide by a fraction, multiply by its reciprocal. Rewrite the division problem as: \[ \frac{x}{5} \div \frac{x+4}{15} = \frac{x}{5} \times \frac{15}{x+4} \]

Step 2: Multiply the Numerators and Denominators

Multiply the numerators together and the denominators together: \[ \frac{x \cdot 15}{5 \cdot (x+4)} = \frac{15x}{5(x+4)} \]

Step 3: Simplify the Fraction

Simplify the fraction by canceling out the common factor of 5 in the numerator and denominator: \[ \frac{15x}{5(x+4)} = \frac{3x}{x+4} \]