5. $$ \frac{2}{x+4}-\frac{1}{x}=\frac{2}{3 x} $$

Question

UpStudy AI · Accepted Answer

Solve the equation $$ \frac{2}{x+4}-\frac{1}{x}=\frac{2}{3x} $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$\frac{2}{x+4}-\frac{1}{x}=\frac{2}{3x}$$
- step1: Find the domain:
  $$\frac{2}{x+4}-\frac{1}{x}=\frac{2}{3x},x \in \left(-\infty,-4ight)\cup \left(-4,0ight)\cup \left(0,+\inftyight)$$
- step2: Multiply both sides of the equation by LCD:
  $$\left(\frac{2}{x+4}-\frac{1}{x}ight)	imes 3x\left(x+4ight)=\frac{2}{3x}	imes 3x\left(x+4ight)$$
- step3: Simplify the equation:
  $$3x-12=2x+8$$
- step4: Move the expression to the left side:
  $$3x-2x=8+12$$
- step5: Add and subtract:
  $$x=8+12$$
- step6: Add and subtract:
  $$x=20$$
- step7: Check if the solution is in the defined range:
  $$x=20,x \in \left(-\infty,-4ight)\cup \left(-4,0ight)\cup \left(0,+\inftyight)$$
- step8: Find the intersection:
  $$x=20$$
The solution to the equation $$ \frac{2}{x+4}-\frac{1}{x}=\frac{2}{3x} $$ is $$ x=20 $$.
$$ x=20 $$

Upstudy AI Solution

Answer

Solution

The Deep Dive

Related Questions

Latest Algebra Questions