Question 202589
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Your rendering of the equation is a bit ambiguous, but I'm going to presume you meant:


6+ (5/(x-1))=6/(x+3) which would look like:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 6 + \frac{5}{x-1}\ =\ \frac{6}{x+3}]


Step 1:  Multiply both sides of the equation by *[tex \Large x - 1]



*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 6(x - 1) + 5\ =\ \frac{6(x - 1)}{x+3}]


Step 2:  Multiply both sides of the equation by *[tex \Large x + 3]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 6(x - 1)(x + 3) + 5(x + 3)\ =\ 6(x - 1)]


Step 3:  Use FOIL and the distributive property:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 6x^2 + 12x -18 + 5x + 15\ =\ 6x - 6]


Step 4:  Collect like terms:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 6x^2 + 11x +3\ =\ 0]


Step 5: Factor:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ (3x + 1)(2x + 3) = 0]


Step 6: Use the Zero Product Rule:  You should be able to handle it from here.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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