How is this complex fraction getting cleared using this method?

Question

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.

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

For the same reason that $\frac {a}{b} - \frac {c}{d} = \frac {ad-bc}{bd}$ ... — Calvin Lin, Feb 08 '13 at 20:03

score 2 · Answer 1 · edited Feb 08 '13 at 20:06

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 $10z - 10x$.

edited Feb 08 '13 at 20:06

Ayman Hourieh

39,603

answered Feb 08 '13 at 20:02

How is this complex fraction getting cleared using this method?

1 Answers1