# Why does $\frac{f(x)}{\frac{f(y)}{h}} = \frac{f(x)}{hf(y)}$

Earlier, I asked a similar question, but this one's getting me confused, as well. Why does $\frac{a}{\frac{b}{x}} = x \times \frac{a}{b}$, but the following expression holds true?

$$\frac{f(x)}{\frac{f(y)}{h}} = \frac{f(x)}{hf(y)}$$

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You did not use parentheses, and Alpha interpreted your question as $\dfrac{\frac{f(x)}{f(y)}}{h}$. Note the thicker "fraction line" in Alpha. Generally, if you don't use parentheses, Alpha reads from left to right. If you want Alpha to operate correctly, use $f(x)/(f(y)/h)$. –  André Nicolas Dec 5 '12 at 6:28

Wolfram Alpha took it as $\frac{\frac{f(x)}{f(y)}}{h}$ instead of $\frac{f(x)}{\frac{f(y)}{h}}$. You need to see which line is longer more carefully. The longer line represents the division performed later.
$$\frac{f(x)}{\frac{f(y)}{h}}\cdot \frac{h}{h}=\frac{f(x)\cdot h}{\frac{f(y)}{h}\cdot h}=\frac{f(x)h}{f(y)}.$$