Think of how you simplify fractions without algebraic terms. (e.g. 1/3 + 2/5. Determine the lowest common multiple between 3 and 5, which is 15.
For the first fraction multiply 5 on both numerator and denominator to get the denominator to 15 and for the second fraction multiply 3 on both numerator and denominator to get the denominator to 15.
Thus, 1/3 + 2/5 = 5/15 + 6/15 = 11/15
The principle for fractions with algebraic terms is the same. The questions asks to simplify (2x)/(x-3) - x/(x+3). Determine the lowest common multiple between x-3 and x+3, which is (x-3)(x+3).
For the first fraction multiply x+3 on both numerator and denominator to get the denominator to (x-3)(x+3) and for the second fraction multiply x-3 on both numerator and denominator to get the denominator to (x-3)(x+3).
Thus,
(2x)/(x-3) - x/(x+3)
=(2x(x+3))/((x-3)(x+3))-(x(x-3))/((x-3)(x+3))
=(2x^2+6x)/((x-3)(x+3))-(x^2-3x)/((x-3)(x+3))
=(2x^2+6x-x^2+3x)/((x-3)(x+3))
=(x^2+9x)/((x-3)(x+3))
=(x(x+9))/((x-3)(x+3))
Always factorise your answer in the end unless the questions asks otherwise.