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Divide. (x^(2)-3xy-18y^(2))/(x^(2)-12 xy+35y^(2))÷(x+3y)/(5x-25 y) Simplify your answer as much as possible

Divide.\newlinex2−3xy−18y2x2−12xy+35y2÷x+3y5x−25y \frac{x^{2}-3 x y-18 y^{2}}{x^{2}-12 x y+35 y^{2}} \div \frac{x+3 y}{5 x-25 y} \newlineSimplify your answer as much as possible

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Multiply and divide rational expressionsright chevron icon

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Q. Divide.\newlinex2−3xy−18y2x2−12xy+35y2÷x+3y5x−25y \frac{x^{2}-3 x y-18 y^{2}}{x^{2}-12 x y+35 y^{2}} \div \frac{x+3 y}{5 x-25 y} \newlineSimplify your answer as much as possible
  1. Factor Numerator and Denominator: Factor both the numerator and the denominator of the first fraction.\newlineNumerator: x2−3xy−18y2x^2 - 3xy - 18y^2 can be factored into (x−6y)(x+3y)(x - 6y)(x + 3y).\newlineDenominator: x2−12xy+35y2x^2 - 12xy + 35y^2 can be factored into (x−5y)(x−7y)(x - 5y)(x - 7y).\newlineNow the expression is (x−6y)(x+3y)(x−5y)(x−7y)×5x−25yx+3y\frac{(x - 6y)(x + 3y)}{(x - 5y)(x - 7y)} \times \frac{5x - 25y}{x + 3y}.
  2. Factor Common Factor: Factor out the common factor in the second fraction's numerator.\newline5x−25y5x - 25y can be factored into 5(x−5y)5(x - 5y).\newlineNow the expression is (x−6y)(x+3y)(x−5y)(x−7y)×5(x−5y)(x+3y)\frac{(x - 6y)(x + 3y)}{(x - 5y)(x - 7y)} \times \frac{5(x - 5y)}{(x + 3y)}.
  3. Cancel Common Factors: Cancel out the common factors in the numerator and the denominator.\newline(x+3y)(x + 3y) cancels out, and (x−5y)(x - 5y) cancels out.\newlineNow the expression is (x−6y)(x−7y)×5\frac{(x - 6y)}{(x - 7y)} \times 5.
  4. Multiply Remaining Factors: Multiply the remaining factors.\newline5×(x−6y)/(x−7y)=5x−30y/(x−7y)5 \times (x - 6y) / (x - 7y) = 5x - 30y / (x - 7y).

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