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[tex]x = 4[/tex]
[tex]\frac{x-4}{2x-5} = 0[/tex]
1. Identify the numerator: For the fraction to equal zero, the numerator must be zero (since a fraction is zero if and only if its numerator is zero while its denominator is non-zero).
[tex]x - 4 = 0[/tex]
2. Solve for ( x ): Set the numerator equal to zero and solve for ( x ).
[tex]x - 4 = 0 \implies x = 4[/tex]
3. Check the solution against the denominator: Ensure that the denominator is not zero for the value of \( x \) that we found.
[tex]2x - 5 \quad \text{when} \quad x = 4 [/tex]
[tex]2(4) - 5 = 8 - 5 = 3[/tex]