(8v)/(28 w+21)-(3v+10)/(4w+3) Which expression is equivalent to the difference? Choose 1 answer: (A) (8v^(2)-21 v+10)/(24 w+18) (B) (-13 v+10)/(24 w+18) (C) (53 v+10)/(28 w+21) (D) (-13 v-70)/(28 w+21)

Question

(8v)/(28 w+21)-(3v+10)/(4w+3) Which expression is equivalent to the difference? Choose 1 answer: (A)  (8v^(2)-21 v+10)/(24 w+18) (B)  (-13 v+10)/(24 w+18) (C)  (53 v+10)/(28 w+21) (D)  (-13 v-70)/(28 w+21)

Bytelearn · Accepted Answer

Identify Common Factor: Identify the common factor between the denominators 28w+21 and 4w+3. Notice that 28w+21 is 7 times 4w+3.Rewrite First Fraction: Rewrite the first fraction with the common denominator. (8v)/(28w+21) can be written as (8v)/(7(4w+3)).Subtract Fractions: Subtract the second fraction from the first fraction, keeping the common denominator in mind. Since the second fraction already has the denominator 4w+3, we can combine the two fractions over a common denominator of 7(4w+3).Combine Numerators: Combine the numerators over the common denominator. (8v)/(7(4w+3)) - (3v+10)/(4w+3) = (8v - 7(3v+10))/(7(4w+3)).Distribute 7: Distribute the 7 in the numerator of the second term. 8v - 7(3v+10) = 8v - 21v - 70.Combine Like Terms: Combine like terms in the numerator. 8v - 21v - 70 = -13v - 70.Write Final Expression: Write the final expression with the simplified numerator and the common denominator. (-13v - 70)/(7(4w+3)) = (-13v - 70)/(28w+21).Match with Answer Choices: Match the final expression with the given answer choices. The final expression (-13v - 70)/(28w+21) matches with choice (D).

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