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