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Which expression is equivalent to
((x+2)/(x^(2)))((x+2)/(3x))?
A.
(x^(2)+4)/(3x^(2))
B.
(x^(2)+4)/(3x^(3))
C.
(x^(2)+4x+4)/(3x^(2))
D.
(x^(2)+4x+4)/(3x^(3))

Which expression is equivalent to $\left(\frac{x+2}{x^{2}}\right)\left(\frac{x+2}{3 x}\right) ?$ $\newline$ A. $\frac{x^{2}+4}{3 x^{2}}$ $\newline$ B. $\frac{x^{2}+4}{3 x^{3}}$ $\newline$ C. $\frac{x^{2}+4 x+4}{3 x^{2}}$ $\newline$ D. $\frac{x^{2}+4 x+4}{3 x^{3}}$

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Multiplication with rational exponents

Full solution

Q. Which expression is equivalent to

\left(\frac{x+2}{x^{2}}\right)\left(\frac{x+2}{3 x}\right) ?

\newline

A.

\frac{x^{2}+4}{3 x^{2}}

\newline

B.

\frac{x^{2}+4}{3 x^{3}}

\newline

C.

\frac{x^{2}+4 x+4}{3 x^{2}}

\newline

D.

\frac{x^{2}+4 x+4}{3 x^{3}}

Simplify Expression: Simplify the expression $\frac{(x+2)}{x^{2}}$ $\frac{(x+2)}{3x}$ . Combine the numerators and denominators. $\frac{(x+2)(x+2)}{x^{2} \cdot 3x}$
Expand and Simplify: Expand the numerator and simplify the denominator. $\newline$ $(x+2)(x+2) = x^2 + 4x + 4$ $\newline$ $x^2 \times 3x = 3x^3$ $\newline$ So, $(x^2 + 4x + 4) / (3x^3)$
Match with Options: Match the simplified expression with the given options. $\newline$ The expression $(x^2 + 4x + 4) / (3x^3)$ matches option $D$ .

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