Proving a equation - im stuck

1. Jun 2, 2007

thomas49th

1. The problem statement, all variables and given/known data
2. Relevant equations
Show that the equation

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

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

3. 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

2. Jun 2, 2007

Coren

Try to guess if the statement is right... for example using the roots of the second equation in the first equation.

3. Jun 2, 2007

steven10137

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

4. Jun 2, 2007

VietDao29

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