What is simplify-2-x+ln|1-1/(-2-x)|+x+ln|1-1/x | ?

The solution to simplify-2-x+ln|1-1/(-2-x)|+x+ln|1-1/x | is ln(|-1/x+1||-1/(-x-2)+1|)-2

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simplify-2-x+ln|1-1/(-2-x)|+x+ln|1-1/x |

simplify

- 2 - x + ln 1 - \frac{1}{- 2 - x} + x + ln 1 - \frac{1}{x}

ln (- \frac{1}{x} + 1 - \frac{1}{- x - 2} + 1) - 2

Solution steps

- 2 - x + ln 1 - \frac{1}{- 2 - x} + x + ln 1 - \frac{1}{x}

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

ln 1 - \frac{1}{- 2 - x} + ln 1 - \frac{1}{x} = ln (- \frac{1}{x} + 1 - \frac{1}{- x - 2} + 1)

= - 2 - x + ln (1 - \frac{1}{- 2 - x} 1 - \frac{1}{x}) + x

Group like terms

= - x + x + ln (- \frac{1}{x} + 1 - \frac{1}{- x - 2} + 1) - 2

Add similar elements:

- x + x = 0

= ln (- \frac{1}{x} + 1 - \frac{1}{- x - 2} + 1) - 2

3 ln (x^{2}) + 5 ln (y) - 2 ln (a) + 4 ln (b^{3}) - 3 ln (c) + 2

\frac{125 \cdot 1.5 \cdot 1 0 ^{6}}{200 \cdot 25 \cdot 50} \cdot ln (\frac{150}{100})

10 \cdot lo g_{10} (\frac{2.7 x 1 0 ^{- 11}}{1 0 ^{- 12}})

- \frac{1}{4} ln ∣ x + 2 ∣ + \frac{1}{4} ln ∣ x - 2 ∣

ln (2) + 2 (ln (2 + 2 - 1)) + ln (3)

What is simplify-2-x+ln|1-1/(-2-x)|+x+ln|1-1/x | ?
The solution to simplify-2-x+ln|1-1/(-2-x)|+x+ln|1-1/x | is ln(|-1/x+1||-1/(-x-2)+1|)-2