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Multiply. Write your answer in simplest form.\newline2y33y+5×5y4y4\frac{2y - 3}{3y + 5} \times \frac{5y - 4}{y - 4}

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Q. Multiply. Write your answer in simplest form.\newline2y33y+5×5y4y4\frac{2y - 3}{3y + 5} \times \frac{5y - 4}{y - 4}
  1. Rewrite Multiplication: Rewrite the multiplication of the two fractions. (2y3)/(3y+5)×(5y4)/(y4)(2y - 3)/(3y + 5) \times (5y - 4)/(y - 4)
  2. Multiply Numerators and Denominators: Multiply the numerators together and the denominators together.\newlineNumerator: (2y3)×(5y4)(2y - 3) \times (5y - 4)\newlineDenominator: (3y+5)×(y4)(3y + 5) \times (y - 4)
  3. Perform Numerator Multiplication: Perform the multiplication in the numerators.\newline(2y3)×(5y4)=10y28y15y+12(2y - 3) \times (5y - 4) = 10y^2 - 8y - 15y + 12\newlineCombine like terms in the numerator.\newline10y223y+1210y^2 - 23y + 12
  4. Perform Denominator Multiplication: Perform the multiplication in the denominators.\newline(3y+5)(y4)=3y212y+5y20(3y + 5) * (y - 4) = 3y^2 - 12y + 5y - 20\newlineCombine like terms in the denominator.\newline3y27y203y^2 - 7y - 20
  5. Combine Numerators and Denominators: Combine the numerators and denominators to form the new fraction. (10y223y+12)/(3y27y20)(10y^2 - 23y + 12)/(3y^2 - 7y - 20)
  6. Check for Further Factorization: Check if the numerator and denominator can be factored further to simplify the fraction.\newlineThe numerator and denominator do not have common factors, and there are no obvious factors that would cancel out between the numerator and denominator.

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