Solving equations (PLEASE help)

[asil223]

I'm stuck on this problem.

(4)/(x+2) - (4)/(x)
__________________ = 1
2

 

[Denis]

I'm stuck on this problem.

(4)/(x+2) - (4)/(x)
__________________ = 1
2

Start this way: (4)/(x+2) - (4)/(x) = 2
Then use LCM:
[4x - 4(x + 2)] / [x(x + 2)] = 2

OK?

 

[soroban]

Hello, asil223!

Is the problem stated correctly?
I'm getting complex answers.

\(\displaystyle \displaystyle \dfrac{\dfrac{4}{x+2} - \dfrac{4}{x}}{2} \;=\;1\)

\(\displaystyle \text{Multiply by 2: }\;\frac{4}{x+2} - \frac{4}{x} \;=\;2\)

\(\displaystyle \text{Multiply by }{x(x+2)\!: \;\;4x - 4(x+2) \;=\;2x(x+2) \quad\Rightarrow\quad 4x - 4x - 8 \:=\:2x^2+4x\)

. . . . . . . . . . . . . . . . \(\displaystyle 2x^2 + 4x + 8 \:=\:0 \quad\Rightarrow\quad x^2 + 2x + 4 \:=\:0\)

\(\displaystyle \text{Quadratic Formula: }\;x \;=\;\dfrac{-2 \pm \sqrt{-12}}{2} \;=\; \dfrac{-2 \pm2i\sqrt{3}}{2} \;=\;-1 \pm i\sqrt{3}\)