21: \(=\dfrac{x\left(x-1\right)\left(x+1\right)}{x\left(x+1\right)^2}=\dfrac{x-1}{x+1}\)
22: \(=\dfrac{\left(x-1\right)^2}{x\left(x-1\right)}=\dfrac{x-1}{x}\)
30: \(=\dfrac{\left(x-1\right)\left(x-2\right)}{x\left(x-1\right)}=\dfrac{x-2}{x}\)
29: =(x-2)(x-3)/(x-2)(x+2)=(x-3)/(x+2)
27: =(x-7)(x+6)/x(x-7)=(x+6)/x
Coi như tất cả các câu đều trên điều kiện xác định.
`21)[x^3-x]/[x^3+2x^2+x]`
`=[x(x^2-1)]/[x(x^2+2x+1)]`
`=[x(x-1)(x+1)]/[x(x+1)^2]`
`=[x-1]/[x+1]`
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`22)[x^2-2x+1]/[x^2-x]`
`=[(x-1)^2]/[x(x-1)]`
`=[x-1]/x`
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`23)[x^2-9y^2]/[x^2-6xy+9y^2]`
`=[(x-3y)(x+3y)]/[(x-3y)^2]=[x+3y]/[x-3y]`
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`24)[3x^3-27x]/[-6x^2+18x]`
`=[3x(x^2-9)]/[-6(x-3)]`
`=[3x(x-3)(x+3)]/[-6(x-3)]=[-x(x+3)]/2=[-x^2-3x]/[2`
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`25)[x^2-4x+4]/[2x^2-4x]`
`=[(x-2)^2]/[2x(x-2)]=[x-2]/[2x]`
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`26)[x^2-2x]/[x^2-4]`
`=[x(x-2)]/[(x-2)(x+2)]`
`=x/[x+2]`
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`27)[x^2-x-42]/[x^2-7x]`
`=[(x-7)(x+6)]/[x(x-7)]`
`=[x+6]/x`
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`28)[3x^2-x-2]/[x^2-1]`
`=[(x-1)(3x+2)]/[(x-1)(x+1)]`
`=[3x+2]/[x+1]`
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`29)[x^2-5x+6]/[x^2-4]`
`=[(x-3)(x-2)]/[(x-2)(x+2)]`
`=[x-3]/[x+2]`
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`30)[x^2-3x+2]/[x^2-x]`
`=[(x-2)(x-1)]/[x(x-1)]`
`=[x-2]/x`
