Multiply. Write your answer in simplest form. 3d + 5/5d^2 * d + 4/3d + 5 ______

Write Problem: Write down the problem to identify the expressions to be multiplied. We have: (3d + 5)/(5d^2) * (d + 4)/(3d + 5)Multiply Expressions: Multiply the numerators together and the denominators together. Expression becomes: ((3d + 5) * (d + 4)) / ((5d^2) * (3d + 5))Expand Numerators/Denominators: Expand the numerators and the denominators. Numerator: (3d + 5) * (d + 4) = 3d^2 + 12d + 5d + 20 = 3d^2 + 17d + 20 Denominator: (5d^2) * (3d + 5) = 15d^3 + 25d^2Write Expanded Expression: Write the expression with the expanded numerator and denominator. Expression becomes: (3d^2 + 17d + 20) / (15d^3 + 25d^2)Cancel Common Factors: Look for common factors in the numerator and the denominator that can be canceled out. There are no common factors between the numerator and the denominator, so the expression is already in its simplest form.Write Final Answer: Write down the final answer. Final answer: (3d^2 + 17d + 20) / (15d^3 + 25d^2)

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Math Problems

Algebra 2

Multiply and divide rational expressions

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Q. Multiply. Write your answer in simplest form.

\newline

\frac{3d + 5}{5d^2} \cdot \frac{d + 4}{3d + 5}

Write Problem: Write down the problem to identify the expressions to be multiplied. $\newline$ We have: $(3d + 5)/(5d^2) \times (d + 4)/(3d + 5)$
Multiply Expressions: Multiply the numerators together and the denominators together. $\newline$ Expression becomes: $\frac{(3d + 5) \cdot (d + 4)}{(5d^2) \cdot (3d + 5)}$
Expand Numerators/Denominators: Expand the numerators and the denominators. $\newline$ Numerator: $(3d + 5) * (d + 4) = 3d^2 + 12d + 5d + 20 = 3d^2 + 17d + 20$ $\newline$ Denominator: $(5d^2) * (3d + 5) = 15d^3 + 25d^2$
Write Expanded Expression: Write the expression with the expanded numerator and denominator. $\newline$ Expression becomes: $(3d^2 + 17d + 20) / (15d^3 + 25d^2)$
Cancel Common Factors: Look for common factors in the numerator and the denominator that can be canceled out. $\newline$ There are no common factors between the numerator and the denominator, so the expression is already in its simplest form.
Write Final Answer: Write down the final answer. $\newline$ Final answer: $(3d^2 + 17d + 20) / (15d^3 + 25d^2)$