The discussion confirms that the expression ##\frac{|x + 1|}{|x + 2|}## is indeed equal to ##\left|\frac{x + 1}{x + 2}\right|## for all values of x except x = -2. Participants demonstrated this equality by testing specific values of x, such as 10 and -10, and concluded that the absolute values can be applied separately to the numerator and denominator without affecting the overall equality. The underlying principle is based on the property of absolute values, specifically ##|xy| = |x||y|##.
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Yes, the two expressions are identically equal.askor said:Is it correct that ##\frac{|x + 1|}{|x + 2|}## equal to ##\left|\frac{x + 1}{x + 2} \right|##?
Think about the expressions x + 1 and x + 2. Each of them is negative, zero, or positive, depending on the value of x. Now, as long as ##x \ne -2##, ##\frac{x +1}{x + 2}## will have some value. Does it matter whether we take the absolute values of the numerator and denominator separately, or evaluate the fraction and then take its absolute value?askor said:Please explain, I don't understand.
Absolutely!askor said:Is it correct that ##\frac{|x + 1|}{|x + 2|}## equal to ##\left|\frac{x + 1}{x + 2} \right|##?