We want to simplify the expression:
[tex]\frac{2x}{x-5}-\frac{x}{x-2}[/tex]First of all, we need to write the expression as a single fraction, this is achievable by taking the common denominator. Doing this, we have:
[tex]\frac{2x(x-2)-x(x-5)}{(x-5)(x-2)}[/tex]Next, we open and simplify the brackets in the numerator.
[tex]\begin{gathered} \frac{2x^2-4x-x^2+5x}{(x-5)(x-2)} \\ =\frac{x^2+x}{(x-5)(x-2)} \\ \end{gathered}[/tex]