# 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

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

4. Jun 2, 2007

### VietDao29

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