Question

problem 16: tell whether these two expressions are equivalent. \\(\frac{x + 7}{5x^3} cdot \frac{15x^2}{2x + 14}\\) and \\(\frac{3}{2x}\\) after you pick your answer press go. yes no go

Explanation:

Step1: Factor the denominator of the second fraction

Factor \(2x + 14\) as \(2(x + 7)\). So the expression becomes \(\frac{x + 7}{5x^3} \cdot \frac{15x^2}{2(x + 7)}\)

Step2: Multiply the numerators and denominators

Multiply the numerators: \((x + 7) \cdot 15x^2 = 15x^2(x + 7)\)
Multiply the denominators: \(5x^3 \cdot 2(x + 7) = 10x^3(x + 7)\)
The expression is now \(\frac{15x^2(x + 7)}{10x^3(x + 7)}\)

Step3: Simplify the fraction

Cancel out the common factors \((x + 7)\) (assuming \(x
eq - 7\)) and simplify the coefficients and variables. \(\frac{15}{10}\times\frac{x^2}{x^3}=\frac{3}{2}\times\frac{1}{x}=\frac{3}{2x}\) (assuming \(x
eq0\))

Answer:

Yes