Lời giải chi tiết:

` 1) (15x)/(7y^3) * (2y^2)/(x^2) `

` = (15x * 2y^2)/(7y^3 * x^2) `

` = (30xy^2)/(7x^2y^3) `

` = 30/(7xy) `

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` 2) (6x^3)/(7y^4) * (35y^2)/(24x) `

` = (6x^3 * 35y^2)/(7y^4 * 24x) `

` = (5x^2)/(4y^2) `

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` 3) (4y^2)/(x^4) * (-3x^2)/(8y) `

` = (4y^2(-3x^2))/(8yx^4) `

` = (-12x^2y^2)/(8x^4y) `

` = (-3y)/(2x^2) `

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` 4) (x^2 - y^2)/(xy) : (x - y)/(xy) `

` = (x^2 - y^2)/(xy) * (xy)/(x - y) `

` = ((x - y)(x + y))/(xy) * (xy)/(x - y) `

` = x + y `

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` 5) (8y^2)/(9x^2) : (4y)/(3x^2) `

` = (8y^2)/(9x^2) * (3x^2)/(4y) `

` = (24x^2y^2)/(36x^2y) `

` = (2y)/3 `

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` 6) (-20x)/(3y^2) : (-4x^3)/(5y) `

` = (-20x)/(3y^2) * (5y)/(-4x^3) `

` = (100xy)/(12x^3y^2) `

` = 25/(3x^2y) `

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` 7) (x^2 - 4)/(x^2 - x) : (x^2 + 2x)/(x - 1) `

` = ((x - 2)(x + 2))/(x(x - 1)) * (x - 1)/(x(x + 2)) `

` = (x - 2)/x `

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` 8) (4(x + 3))/(3x^2 - x) * (x^2 + 3x)/(1 - 3x) `

` = (4(x + 3))/(x(3x - 1)) * (x(x + 3))/(-(3x - 1)) `

` = (-4(x + 3)^2)/((3x - 1)^2) `

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` 9) (4x + 12)/((x + 4)^2) : (3(x + 3))/(x + 4) `

` = (4(x + 3))/((x + 4)^2) * (x + 4)/(3(x + 3)) `

` = 4/(3(x + 4)) `