simplify the complex fraction. y -1/ y2 + y -6 over y-6/y+3?

3 Answers

  • (y – 1)/(y^2 + y – 6) / ((y – 6)/(y + 3))

    = (y – 1)/((y + 3)(y – 2)) / ((y – 6)/(y + 3))

    = (y – 1)/((y – 2)(y – 6))

  • Break the complex fraction up into division:

    (y – 1) / (y^2 + y – 6) ÷ (y – 6) / (y + 3)

    Factor out as much as possible:

    (y – 1) / (y + 3)(y – 2) ÷ (y – 6) / (y + 3)

    Like you would in normal fractional divison, flip the second fraction and multiply:

    (y – 1) / (y + 3)(y – 2) x (y + 3) / (y – 6)

    When multiplying fractions you can simplify either vertically or diagonally, NEVER horizontally. So simplify the (y + 3) and (y + 3):

    (y – 1) / (y – 2) x 1 / (y – 6)

    Now multiply the numerators and denominators into each other:

    (y – 1) / (y – 2)(y – 6)

  • Note that brackets MUST be used.

    (y – 1) / (y² + y – 6)

    —————————

    (y – 6) / (y + 3)

    (y – 1) (y + 3)

    ———————–

    (y – 6) (y + 3)(y – 2)

    y – 1

    —————-

    (y – 6) (y – 2)

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