(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)

Question

(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)

Bytelearn · Accepted Answer

Identify Given Expression: Identify the given expression and look for common factors that can be simplified. The expression is (3g^(2)+12 g)/(g+7)*(4)/(8g^(2)).Factor Out Common Factor: Factor out the common factor in the numerator of the first fraction. 3g^(2)+12 g = 3g(g+4).Rewrite with Factored Numerator: Rewrite the expression with the factored numerator. (3g(g+4))/(g+7)*(4)/(8g^(2)).Simplify by Canceling Factors: Simplify the expression by canceling out common factors in the numerator and the denominator. The 4 in the numerator and the 8 in the denominator can be simplified to 1/2. (3g(g+4))/(g+7)*(1/2)/(g^(2)).Combine Fractions by Multiplying: Combine the two fractions by multiplying the numerators and denominators. (3g(g+4)*1)/(2*(g+7)*g^(2)).Distribute Across Numerator: Distribute the 3g across (g+4) in the numerator. (3g^2+12g)/(2*(g+7)*g^(2)).Simplify Denominator: Simplify the denominator by multiplying the terms. (3g^2+12g)/(2g^3+14g^2).Look for Common Factors: Look for common factors in the numerator and denominator that can be canceled out. There are no common factors other than g, which cannot be canceled out because it would change the domain of the original expression (g > 0).Rewrite in Answer Choice Form: Rewrite the expression in the form of one of the answer choices. (3g+12)/(2g^2+14g) matches answer choice (C).

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