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

Question

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

Abigail Allen · Accepted Answer

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

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.

Eva Adamson · Answer

undefined To simplify the expression (2x+3)/(x^2-9) + x/(x-3), we first need to factor the denominators. The denominator x^2-9 can be factored as (x-3)(x+3).

Now, we can find a common denominator for the two fractions, which is (x-3)(x+3).

Next, we multiply the numerator and denominator of the first fraction (2x+3) by (x-3), and the numerator and denominator of the second fraction (x) by (x+3).

After simplifying, we get (2x+3)(x-3)/(x-3)(x+3) + x(x+3)/(x-3)(x+3).

Combining the fractions, we have [(2x+3)(x-3) + x(x+3)]/(x-3)(x+3).

Expanding and simplifying the numerator, we get (2x^2 - 3x - 9 + x^2 + 3x)/(x-3)(x+3).

Combining like terms, we have (3x^2 - 9)/(x-3)(x+3).

Finally, we can further simplify by factoring the numerator, resulting in 3(x^2 - 3)/(x-3)(x+3).

Therefore, the simplified expression is 3(x^2 - 3)/(x-3)(x+3).