Question 178222
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*[tex \Large {3 \over x} - {1 \over 6} = {1 \over x}]


LCD is 6x:


*[tex \Large {18 \over 6x} - {x \over 6x} = {6 \over 6x}]


Multiply both sides by 6x:


*[tex \Large 18 - x = 6]


*[tex \Large - x = -12]


*[tex \Large x = 12]


Check:


*[tex \Large {3 \over 12} - {1 \over 6} = {1 \over 12}]


*[tex \Large {3 \over 12} - {2 \over 12} = {1 \over 12}]


Answer checks.


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*[tex \Large x + 5 = {6 \over x]


Multiply both sides by x, then add -6 to both sides:


*[tex \Large x^2 + 5x - 6 = 0]


Factor:


*[tex \Large (x - 1)(x + 6) = 0]


So:


*[tex \Large x = 1] or *[tex \Large x = -6]


Check:


*[tex \Large 1 + 5 = {6 \over 1}] Checks.



*[tex \Large -6 + 5 = {6 \over -6}]  Checks.


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