Đáp án:

Bài `4.`

`a)` `{15x.(x + y)^3}/{5y.(x + y)^2}`

`= {5.3y.(x + y).(x + y)^2}/{5y.(x + y)^2}`

`= {3.(x + y)}/{y}`

`= {3x + 3y}/y`

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`b)` `{5.(x - y) - 3x.(y - x)}/{10.(x - y)}`

`= {5.(x - y) + 3x.(x - y)}/{10.(x - y)}`

`= {(x - y).(5 + 3x)}/{10.(x - y)}`

`= {5 +3x}/10`

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`c)` `{x^2 - xy}/{3xy - 3y^2}`

`= {x.(x - y)}/{3y.(x - y)}`

`= x/{3y}`

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`d)` `{x^2 + 4y^2 - 4xy - 4}/{2x^2 - 4xy + 4x}`

`= {(x^2 - 4xy + 4y^2) - 4}/{2x.(x - 2y + 2)}`

`= {(x - 2y)^2 - 2^2}/{2x.(x - 2y + 2)}`

`= {(x -2y - 2).(x - 2y + 2)}/{2x.(x - 2y + 2)}`

`= {x - 2y -2}/{2x}`

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`e)` `{5x^2 + 10xy + 5y^2}/{3x^3 + 3y^3}`

`= {5.(x^2 + 2xy + y^2)}/{3.(x^3 + y^3)}`

`= {5.(x + y)^2}/{3.(x + y).(x^2 - xy + y^2)}`

`= {5.(x + y)}/{3.(x^2 - xy + y^2)}`

`= {5x + 5y}/{3x^2 - 3xy + 3y^2}`

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`f)` `{-15x.(x-  y)}/{3.(y - x)}`

`= {15x.(y - x)}/{3.(y - x)}`

`= {3.5x.(y - x)}/{3.(y - x)}`

`= 5x`