How do you simplify (2x+3)/(x^2-9) + x/(x-3)?

1 Answer
Feb 19, 2016

(x^2 +5x+3)/((x-3)(x+3))

Explanation:

Note: To add fraction, we need common denominator
Remember:factor of the difference of square
(a^2 -b^2) = (a-b)(a+b)

Here is how we can simplify (2x+3)/(x^2-9) + x/(x-3)

Step 1 : Factor the denominator

(2x+3)/((x-3)(x+3)) + x/(x-3)

Step 2: Find the common denominator

(2x+3)/((x-3)(x+3)) + x/(x-3)color(red)(((x+3)/(x+3))

Step 3: Multiply

(2x+3)/((x-3)(x+3)) + (x^2 +3x)/((x-3)(x+3))

Step 4: Combined like terms

(x^2 +5x+3)/((x-3)(x+3))

We can't factor the numerator, therefore the answer stay as it is.