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.