Solve the Fraction Equation: x^2/3 + 4/3 = 3(x - 2)(x + 2)

Resolve:

x2+43=3(x−2)(x+2) \frac{x^2+4}{3}=3(x-2)(x+2)

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Resolve:

x2+43=3(x−2)(x+2) \frac{x^2+4}{3}=3(x-2)(x+2)

2

Step-by-step solution

To solve the equation x2+43=3(x−2)(x+2) \frac{x^2 + 4}{3} = 3(x-2)(x+2) , we will follow these steps:

  • Step 1: Remove the fraction by multiplying both sides by 3.
  • Step 2: Expand and simplify the right side using the difference of squares.
  • Step 3: Rearrange into a standard quadratic form.
  • Step 4: Solve the quadratic equation.

Let's begin:

Step 1: Multiply both sides by 3 to eliminate the fraction:

x2+4=9(x−2)(x+2) x^2 + 4 = 9(x-2)(x+2)

Step 2: Recognize that (x−2)(x+2) (x-2)(x+2) is a difference of squares:

(x−2)(x+2)=x2−4 (x-2)(x+2) = x^2 - 4

Then we have:

x2+4=9(x2−4) x^2 + 4 = 9(x^2 - 4)

Step 3: Distribute the 9 on the right side:

x2+4=9x2−36 x^2 + 4 = 9x^2 - 36

Step 4: Rearrange this into a standard quadratic form:

x2−9x2=−36−4 x^2 - 9x^2 = -36 - 4

Simplify:

−8x2=−40 -8x^2 = -40

Divide everything by -8 to solve for x2 x^2 :

x2=5 x^2 = 5

Step 5: Solve by taking the square root of both sides:

x=±5 x = \pm \sqrt{5}

Therefore, the solution to the problem is x=±5 x = \pm \sqrt{5} .

3

Final Answer

±⁡5 \operatorname{\pm}\sqrt{5}

Practice Quiz

Test your knowledge with interactive questions

Solve:

\( (2+x)(2-x)=0 \)

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Short Multiplication Formulas questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

More Questions

Click on any question to see the complete solution with step-by-step explanations

Difference of squares

Solve the Fraction Equation: Find x in (x²-9)/(x-3) = 0
Click to solve
Solve the Algebraic Expression: (x-8)(x+8) + 3x + 17 = -49
Click to solve