Question

find the quotient.
\\(\frac{x + 4}{x^2} div \frac{2}{x}\\)
a. \\(\frac{2x}{x + 4}\\)
b. \\(\frac{2x^2}{x + 4}\\)
c. \\(\frac{x + 4}{2x}\\)
d. \\(\frac{x + 4}{2x^2}\\)

Explanation:

Step1: Recall division of fractions rule

To divide two fractions, we multiply the first fraction by the reciprocal of the second fraction. So, \(\frac{x + 4}{x^2}\div\frac{2}{x}=\frac{x + 4}{x^2}\times\frac{x}{2}\).

Step2: Simplify the multiplication

Multiply the numerators and denominators: \(\frac{(x + 4)\times x}{x^2\times2}\). Then, cancel out the common factor \(x\) in the numerator and denominator (since \(x^2=x\times x\), we can cancel one \(x\) from numerator and denominator). This gives \(\frac{x + 4}{2x}\).

Answer:

C. \(\frac{x + 4}{2x}\)