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Can I split the modulus of a rational function into two parts like this

$$ \left|\frac{f(x)}{g(x)}\right|=\frac{\left|f(x)\right|}{\left|g(x)\right|} \ $$

Is this statement always true for any function (or at least for polynomials)

Thanks

mathreadler
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NumberCruncher
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    Yes. Of course, we need $g(x) \neq 0$ for the equation to be well-defined. – MathematicsStudent1122 Jul 04 '17 at 12:26
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    related: https://math.stackexchange.com/questions/633642/prove-that-the-absolute-value-of-a-product-is-the-product-of-the-absolute-values and https://math.stackexchange.com/questions/1373103/fxgx-fxgx – Henry Jul 04 '17 at 12:27
  • Equivalent is not the right word, maybe you mean equal. Equivalent you use to say that two relations are the same. But there are no relations involved here. – mathreadler Jul 04 '17 at 12:39
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    Is that true for any two given real numbers ? $|\frac{a}{b}| = \frac{|a|}{|b|}$? – leonbloy Jul 04 '17 at 12:47
  • @leonbloy I know it would always be true for number so I suppose it should be for functions too, since functions give out some numbers. Thanks for the answer. – NumberCruncher Jul 04 '17 at 12:53
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    @mathreadler Thanks for editing my post, I managed to figure out how to do fractions, but how do you get the absolute value sign? – NumberCruncher Jul 04 '17 at 12:54
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    @NumberCruncher: It is "\left| hey \right|" $\to \left| hey \right|$ the left and right adjust the height correctly, if you are not concerned with height of the expression you can just use "|hey|" but it will look strange if you have fractions since they are usually higher than usual height. – mathreadler Jul 04 '17 at 12:55
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    @mathreadler \left| Thank \right| you for that – NumberCruncher Jul 04 '17 at 12:59

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