Answer:
[tex]\dfrac{1}{x-4}[/tex]
Step-by-step explanation:
The given expression is
[tex]\dfrac{x-5}{(x-5)(x-4)}[/tex]
We need to find an expression which is equivalent to the given expression.
In the given expression (x-5) is common in numerator and denominator.
The given expression can be written as
[tex]\dfrac{x-5}{x-5}\times \dfrac{1}{x-4}[/tex]
Cancel out the common factors.
[tex]1\times \dfrac{1}{x-4}[/tex]
[tex]\dfrac{1}{x-4}[/tex]
Therefore, the expression [tex]\dfrac{1}{x-4}[/tex] is equivalent to the given expression.
