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Divide. Write your answer in simplest form. \newline4y+1y2÷(2y−1)\frac{4y + 1}{y^2} \div (2y - 1)

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Multiply and divide rational expressionsright chevron icon

Full solution

Q. Divide. Write your answer in simplest form. \newline4y+1y2÷(2y−1)\frac{4y + 1}{y^2} \div (2y - 1)
  1. Rewrite as multiplication: Rewrite the division as a multiplication by taking the reciprocal of the divisor. So, (4y+1)/y2÷(2y−1)(4y + 1)/y^2 \div (2y - 1) becomes (4y+1)/y2×1/(2y−1)(4y + 1)/y^2 \times 1/(2y - 1).
  2. Multiply numerators and denominators: Multiply the numerators and then multiply the denominators. So, (4y+1)/y2×1/(2y−1)(4y + 1)/y^2 \times 1/(2y - 1) becomes (4y+1)×1/(y2×(2y−1))(4y + 1) \times 1 / (y^2 \times (2y - 1)).
  3. Simplify expression: Simplify the expression if possible. In this case, there are no common factors to cancel out, so the expression remains as is: (4y+1)/(y2(2y−1))(4y + 1) / (y^2(2y - 1)).
  4. Final answer: Write the answer in the simplest form. The expression is already in its simplest form, so the final answer is (4y+1)/(y2(2y−1))(4y + 1) / (y^2(2y - 1)).

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