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Factor out the common factor from the numerator.

Mathematics

ScanSolve AI Answer

Answer

x−y3x+y\frac{x - y}{3x + y}

Step-by-step solution

5 steps

  1. Factor out the common factor from the numerator.

    6x2−8xy+2y2=2(3x2−4xy+y2)6x^2 - 8xy + 2y^2 = 2(3x^2 - 4xy + y^2)

  2. Factor the quadratic expression in the parenthesis in the numerator.

    3x2−4xy+y2=(3x−y)(x−y)3x^2 - 4xy + y^2 = (3x - y)(x - y)

    So the numerator becomes:

    2(3x−y)(x−y)2(3x - y)(x - y)

  3. Factor out the common factor from the denominator.

    18x2−2y2=2(9x2−y2)18x^2 - 2y^2 = 2(9x^2 - y^2)

  4. Factor the expression in the parenthesis in the denominator using the difference of squares formula, a2−b2=(a−b)(a+b)a^2 - b^2 = (a - b)(a + b).

    9x2−y2=(3x)2−y2=(3x−y)(3x+y)9x^2 - y^2 = (3x)^2 - y^2 = (3x - y)(3x + y)

    So the denominator becomes:

    2(3x−y)(3x+y)2(3x - y)(3x + y)

  5. Substitute the factored expressions back into the fraction and simplify by canceling common factors.

    2(3x−y)(x−y)2(3x−y)(3x+y)=x−y3x+y\frac{2(3x - y)(x - y)}{2(3x - y)(3x + y)} = \frac{x - y}{3x + y}

    The simplified expression is x−y3x+y\frac{x - y}{3x + y}.

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