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Can someone please explain how multiplying these two fractions together is clearing the complex fraction? I know that by multiplying these two fractions clears the complex fraction, I just can't figure out how it works.

$$\frac{\dfrac{5z}{z+2}-\dfrac{5x}{x+2}}{z-x}\cdot \frac{(z+2)(x+2)}{(z+2)(x+2)} = \frac{10z-10x}{(x-z)(z+2)(x+2)}$$

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  • $\begingroup$ For the same reason that $\frac {a}{b} - \frac {c}{d} = \frac {ad-bc}{bd}$ ... $\endgroup$ – Calvin Lin Feb 8 '13 at 20:03
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Recall the distributive property; the numerator will become

$$ \frac{5z}{z + 2} (z + 2)(x + 2) - \frac{5x}{x + 2} (z + 2)(x + 2) = 5z (x + 2) - 5x (z + 2) $$

Now cancelling the fractions and simplifying will give $10z - 10x$.

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