- #1

askor

- 166

- 9

Please explain, I don't understand.

Thank you

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- Thread starter askor
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- #1

askor

- 166

- 9

Please explain, I don't understand.

Thank you

- #2

jedishrfu

Mentor

- 14,294

- 8,340

I pick x = 10

|x+1| / |x+2| = |11| / |12| = 11 / 12 = | 11/12 | = | (x+1) / (x+2) |

then pick x=-10

| x+1| / |x+2| = |-9| / |-8| = 9 / 8 = | 9/8 | = | -9/-8 | = | (x+1) / (x+2) |

Try other values for x and then decide if it is true or not.

- #3

Mark44

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- 8,936

Yes, the two expressions are identically equal.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.

- #4

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- 15,753

Absolutely!Is it correct that ##\frac{|x + 1|}{|x + 2|}## equal to ##\left|\frac{x + 1}{x + 2} \right|##?

It's only ##|xy| = |x||y|## in disguise.

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