Understanding the Equation
The given equation is:
1/a + b + x = 1/a + 1/b + 1/x
To solve or simplify this equation, let’s break it down into manageable parts.
Step 1: Analyzing Both Sides
- The left side includes terms 1/a, b, and x.
- The right side contains 1/a, 1/b, and 1/x.
Step 2: Simplifying the Equation
- Since 1/a is present on both sides, we can eliminate it from the equation.
- This leads us to:
b + x = 1/b + 1/x
Step 3: Rearranging the Equation
- Rearranging gives us:
b + x - 1/b - 1/x = 0
Step 4: Finding a Common Denominator
- The common denominator for the fractions 1/b and 1/x is bx:
- Multiply through by the common denominator (bx) to eliminate the fractions:
b^2x + bx^2 - x - b = 0
Step 5: Factoring the Equation
- This is a quadratic equation in terms of either b or x, which can be factored or solved using the quadratic formula.
Conclusion
- The original equation represents a balance between the sum of variables on both sides.
- Solving it requires rearranging and factoring to find values for a, b, and x that satisfy the equation.
This approach helps in understanding how to manipulate equations effectively, a crucial skill in algebra!