Think of how you simplify fractions without algebraic terms. (e.g. 1/3 + 2/513+25. Determine the lowest common multiple between 33 and 55, which is 1515.
For the first fraction multiply 55 on both numerator and denominator to get the denominator to 1515 and for the second fraction multiply 33 on both numerator and denominator to get the denominator to 1515.
Thus, 1/3 + 2/5 = 5/15 + 6/15 = 11/1513+25=515+615=1115
The principle for fractions with algebraic terms is the same. The questions asks to simplify (2x)/(x-3) - x/(x+3)2xx−3−xx+3. Determine the lowest common multiple between x-3x−3 and x+3x+3, which is (x-3)(x+3)(x−3)(x+3).
For the first fraction multiply x+3x+3 on both numerator and denominator to get the denominator to (x-3)(x+3)(x−3)(x+3) and for the second fraction multiply x-3x−3 on both numerator and denominator to get the denominator to (x-3)(x+3)(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.
