Toán 8 phân thức

haphuongnb6@gmail.com said:

A = (x+2/x^2-2x + x-6/x^2-4 - x-2/x^2+2x) : 2x-7/x^2-4x+4
a, rút gọn A
b, Tìm x nguyên để A nhận gt nguyên

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[tex](\frac{x+2}{x^2-2x}+\frac{x-6}{x^2-4}-\frac{x-2}{x^2+2x}):\frac{2x-7}{x^2-4x+4}[/tex]
ĐKXD:[tex]x\neq2[/tex] [tex]x\neq -2[/tex]
=[tex](\frac{(x+2)^2}{x(x+2)(x-2)}+\frac{x(x-6)}{x(x+2)(x-2)}-\frac{(x-2)^2}{x(x+2)(x-2)}):\frac{2x-7}{(x-2)^2}[/tex]
=[tex](\frac{x^2+4x+4+x^2-6x-x^2+4x-4}{x(x+2)(x-2)}):\frac{2x-7}{(x-2)^2}[/tex]
=[tex](\frac{x^2+2x}{x(x+2)(x-2)}):\frac{2x-7}{(x-2)^2}[/tex]
=[tex](\frac{x(x+2)}{x(x+2)(x-2)}).\frac{(x-2)^2}{2x-7}[/tex]
=[tex]\frac{x(x-2)}{x(2x-7)}[/tex]