(x-3)(x-4)(x-5)=(x-2)(x-4)(x-5)

Jasonbradley

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Jun 17, 2024

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Solving the Equation (x-3)(x-4)(x-5) = (x-2)(x-4)(x-5)

This equation presents a unique situation where we can find the solutions by carefully analyzing the factors involved.

Understanding the Factors

• Common Factors: Notice that both sides of the equation share the factors (x-4) and (x-5).
• Cancellation: Since these factors are identical on both sides, we can cancel them out, leaving us with:

(x-3) = (x-2)

Finding the Solution

This simplified equation now leads us to a clear conclusion:

• No Solution: The equation (x-3) = (x-2) is not possible, as subtracting 3 from a number can never result in the same outcome as subtracting 2.

Conclusion

Therefore, the original equation (x-3)(x-4)(x-5) = (x-2)(x-4)(x-5) has no solution. This is because the cancellation of common factors reveals an impossible equation.