Proving a Equation: Solving for x in 2/(x+1) + 1/(x+2) = 1/2

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The equation 2/(x+1) + 1/(x+2) = 1/2 can be transformed into x² + x - 4 = 0. The initial attempt at solving led to the equation x² - 3x - 8 = 0, which was incorrectly deemed wrong by the poster. However, it was confirmed that their working was correct, and the book's provided solution was inaccurate. The discussion highlights the importance of verifying solutions against the original equation.
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Homework Statement


Homework Equations


Show that the equation

\frac{2}{x+1}+\frac{1}{x+2} = \frac{1}{2}

can be written as x^{2} + x - 4 = 0





The Attempt at a Solution



mulitply the fractions on the LHS numerators by opposite denominators and multiply denominators togethter giving me:

\frac{3x + 5}{x^{2} + 3x + 2} = \frac{1}{2}

cross multiply

x^{2} + 3x + 2 = 6x + 10
which is rearanged to give x^{2} - 3x - 8 = 0

which is wrong :(

Where have I gone wrong
Thx
 
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Try to guess if the statement is right... for example using the roots of the second equation in the first equation.
 
indeed, your working is correct.

the question stated is obviously incorrect ...

When you place the roots found from your equation x^{2} - 3x - 8 = 0 as Coren said back into the equation, the solution is 1/2

Steven
 
thomas49th said:
x^{2} + 3x + 2 = 6x + 10
which is rearanged to give x^{2} - 3x - 8 = 0

which is wrong :(

Where have I gone wrong
Thx

Nope, it's totally correct. The answer the book gives is wrong.
So, congratulations. :)
 

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