1/(x-5y)－1/(x-6y)－1/(x-8y)＋1/(x-9y)
=1/(x-5y)－1/(x-8y)＋1/(x-9y)－1/(x-6y)
=[(x-8y)-(x-5y)]/[(x-5y)(x-8y)]+[(x-6y)-(x-9y)]/[(x-9y)(x-6y)]
=(-3y)/[(x-5y)(x-8y)]+ 3y/[(x-9y)(x-6y)]
=3y*{ 1/[(x-9y)(x-6y)] - 1/[(x-5y)(x-8y)] }
=3y*[(x-5y)(x-8y) - (x-9y)x-6y)]/[(x-9y)(x-6y)(x-5y)(x-8y)]
=3y*[(x²-13xy+40y²)-(x²-15xy+54y²)]/[(x-9y)(x-6y)(x-5y)(x-8y)]
=3y*(2xy-14y²)/[(x-9y)(x-6y)(x-5y)(x-8y)]
=6y²(x-7y)/[(x-9y)(x-6y)(x-5y)(x-8y)]