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

[thomas49th]

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

 

[Coren]

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

 

[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

 

[VietDao29]

$$x^{2} + 3x + 2 = 6x + 10$$
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. :)