How do I simplify (2x)/(x-3)-(x)/(x+3)?

1 Answer
Aug 9, 2015

(x(x+9))/((x-3)(x+3))

Explanation:

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.