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Multiply. Write your answer in simplest form.\newline4y−3y×(y−1)\frac{4y - 3}{y} \times (y - 1)

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Multiply and divide rational expressionsright chevron icon

Full solution

Q. Multiply. Write your answer in simplest form.\newline4y−3y×(y−1)\frac{4y - 3}{y} \times (y - 1)
  1. Rewrite multiplication: Rewrite the multiplication of the two fractions. \newlineCalculation: (4y−3y)×(y−11)(\frac{4y - 3}{y}) \times (\frac{y - 1}{1}).
  2. Multiply numerators and denominators: Multiply the numerators together and the denominators together.\newlineCalculation: Numerator = (4y−3)×(y−1)(4y - 3) \times (y - 1), Denominator = y×1y \times 1.
  3. Expand using distributive property: Expand the numerator using the distributive property.\newlineCalculation: (4y−3)×(y−1)=4y(y)−4y(1)−3(y)+3(1)=4y2−4y−3y+3(4y - 3) \times (y - 1) = 4y(y) - 4y(1) - 3(y) + 3(1) = 4y^2 - 4y - 3y + 3.
  4. Combine like terms: Combine like terms in the expanded numerator.\newlineCalculation: 4y2−4y−3y+3=4y2−7y+34y^2 - 4y - 3y + 3 = 4y^2 - 7y + 3.
  5. Write simplified fraction: Write the simplified numerator over the denominator.\newlineCalculation: (4y2−7y+3)/y(4y^2 - 7y + 3)/y.
  6. Check for common factors: Check if the numerator and denominator have any common factors that can be canceled out.\newlineSince yy is a factor of the denominator and there is no yy term that can be factored out from the numerator, we cannot simplify further.

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