Simplify: [(x2 - x - 6) / (y2 + 3y - 10)] · [(y2 - 7y + 10) / (3x2 + x - 10)] ÷ [(x2 - 2x - 3) / (9x2 - 25)]

Answer 1

Step 1: Express the division of the 3rd fraction as multiplication:
[(x2 - x - 6) / (y2 + 3y - 10)] · [(y2 - 7y + 10) / (3x2 + x - 10)] · [(9x2 - 25) / (x2 - 2x - 3)]

Step 2: Factor out each binomial:
x2 - x - 6: (x + 2) (x - 3)
y2 + 3y - 10: (y - 2)(y + 5)
y2 - 7y + 10: (y - 2)(y - 5)
3x2 + x - 10: (3x - 5)(x + 2)
9x2 - 25: (3x + 5)(3x - 5)
x2 - 2x - 3: (x - 3)(x + 1)

Step 3: Combine into 1 big fraction, using the factors we just derived in step 2. Numerators are all on top, denominators all on the bottom.
(x + 2)(x - 3)(y - 2)(y - 5)(3x + 5)(3x - 5)
-----------------------------------------------------------------------
(y - 2)(y + 5)(3x - 5)(x + 2)(x - 3)(x + 1)

Step 4: Cancel out terms that are on the top and bottom:
(y-2), (x+2), (x-3), (3x-5) all cancel, leaving:
(y - 5)(3x + 5)
--------------------------
(y + 5)(x + 1)

Step 5: Multiply out the factors:
3xy - 15x + 5y - 25
------------------------------- (solution!)
xy + 5x + y + 5

Answer 2

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