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(3g^(2)+12 g)/(g+7)*(4)/(8g^(2))
Which expression is equivalent to the product for all
g > 0 ?
Choose 1 answer:
(A)
(3g+48)/(g^(2)+56 g)
(B)
(12 g+12)/(8g^(2)+7g)
(c)
(3g+12)/(2g^(2)+14 g)
(D)
(3+12 g)/(2g+14)

$\frac{3 g^{2}+12 g}{g+7} \cdot \frac{4}{8 g^{2}}$ $\newline$ Which expression is equivalent to the product for all g>0 ? $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{3 g+48}{g^{2}+56 g}$ $\newline$ (B) $\frac{12 g+12}{8 g^{2}+7 g}$ $\newline$ (C) $\frac{3 g+12}{2 g^{2}+14 g}$ $\newline$ (D) $\frac{3+12 g}{2 g+14}$

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Compare linear and exponential growth

Full solution

Q.

\frac{3 g^{2}+12 g}{g+7} \cdot \frac{4}{8 g^{2}}

\newline

Which expression is equivalent to the product for all

g>0

?

\newline

Choose

1

answer:

\newline

(A)

\frac{3 g+48}{g^{2}+56 g}

\newline

(B)

\frac{12 g+12}{8 g^{2}+7 g}

\newline

(C)

\frac{3 g+12}{2 g^{2}+14 g}

\newline

(D)

\frac{3+12 g}{2 g+14}

Factor Common Factor: First, let's factor out the common factor in the numerator of the first fraction. $\newline$ $3g^2 + 12g$ can be factored as $3g(g + 4)$ . $\newline$ So, the expression becomes $(3g(g + 4))/(g + 7) \times (4)/(8g^2)$ .
Simplify Second Fraction: Next, we simplify the second fraction by dividing both the numerator and the denominator by $4$ . $\newline$ $(4)/(8g^2)$ simplifies to $(1)/(2g^2)$ . $\newline$ Now, the expression is $(3g(g + 4))/(g + 7) \times (1)/(2g^2)$ .
Multiply Fractions: We can now multiply the two fractions together. $\newline$ When multiplying fractions, we multiply the numerators together and the denominators together. $\newline$ $(3g(g + 4))/(g + 7) \times (1)/(2g^2)$ becomes $(3g(g + 4))/(2g^2(g + 7))$ .
Cancel Simplify: We can simplify the expression by canceling out a $g$ from the numerator and the $g^2$ in the denominator. $\newline$ This leaves us with $(3(g + 4))/(2g(g + 7))$ .
Distribute Numerator Denominator: Now, we distribute the $3$ in the numerator and the $2g$ in the denominator. $\newline$ This gives us $(3g + 12)/(2g^2 + 14g)$ .
Check Answer Choices: We check the answer choices to see which one matches our simplified expression. $\newline$ The correct answer is (C) $(3g + 12)/(2g^2 + 14g)$ .

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\newline

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\newline

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\newline

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\newline

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