Question

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

Answer 1

`(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.