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The main property of a fraction. Reducing Fractions

Fundamental property of a fraction: if the numerator and denominator are multiplied or divided by the same nonzero expression, the value of the fraction does not change. For algebraic fractions, reduction is done by factoring.
You may cancel only common factors
Do not cancel parts of sums and differences term by term
Always respect restrictions on the denominator
Reduce the algebraic fraction.
Fraction reduction
6x29x\frac{6x^2}{9x}
=2x3, x0=\frac{2x}{3},\ x\neq0
6x29x=6xx9x\frac{6x^2}{9x}=\frac{6\cdot x\cdot x}{9\cdot x}=6x9=\frac{6x}{9}=2x3=\frac{2x}{3}
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