Answer:
x
Step-by-step explanation:
Let's simplify the LHS so it can be equated to the RHS.
[tex]\frac{x}{x^{2} -4x+4} - \frac{x}{x^{2} -3x+2}[/tex]
[tex]\frac{x}{(x-2)^{2} } - \frac{x}{(x-1)(x-2)}[/tex]
[tex]\frac{x(x-1)-x(x-2)}{(x-2)^{2}(x-1)}[/tex]
[tex]\frac{x^{2} -x-x^{2}+2x }{(x-2)^{2}(x-1)}[/tex]
[tex]\frac{x}{(x-2)^{2}(x-1)}[/tex]
Hence, the missing term in the numerator of the answer is x
