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Solving the Equation: (x+2)^2 / (2x-3) - 1 = (x^2+10) / (2x-3)
This article will guide you through the steps of solving the equation:
(x+2)^2 / (2x-3) - 1 = (x^2+10) / (2x-3)
1. Simplifying the Equation
To begin, we need to simplify the equation. Let's combine the terms on the left side:
(x+2)^2 / (2x-3) - (2x-3) / (2x-3) = (x^2+10) / (2x-3)
Now, we can combine the numerators on the left side:
[(x+2)^2 - (2x-3)] / (2x-3) = (x^2+10) / (2x-3)
2. Expanding and Combining Terms
Next, we expand the square on the left side:
(x^2 + 4x + 4 - 2x + 3) / (2x-3) = (x^2+10) / (2x-3)
Combining like terms, we get:
(x^2 + 2x + 7) / (2x-3) = (x^2+10) / (2x-3)
3. Eliminating the Denominators
Since both sides of the equation have the same denominator, we can multiply both sides by (2x-3) to eliminate the denominators:
(x^2 + 2x + 7) = (x^2 + 10)
4. Solving for x
Now, we can solve for x by simplifying the equation further:
2x + 7 = 10
2x = 3
x = 3/2
Conclusion
Therefore, the solution to the equation (x+2)^2 / (2x-3) - 1 = (x^2+10) / (2x-3) is x = 3/2.