Answer:
\(\frac{3x^2+22x+30}{(2x+3)*(x+2)}\)
Step-by-step explanation:
We have been given an expression \(\frac{x+9}{2x+3}+\frac{x+4}{x+2}\). We are asked to simplify our given expression.
First of all, we will make a common denominator as shown below:
\(\frac{(x+9)*(x+2)}{(2x+3)*(x+2)}+\frac{(x+4)*(2x+3)}{(x+2)*(2x+3)}\)
Now, we will use distributive property to solve our expression as:
\(\frac{x(x+2)+9(x+2)}{(2x+3)*(x+2)}+\frac{x(2x+3)+4(2x+3)}{(x+2)*(2x+3)}\)
\(\frac{x^2+2x+9x+18}{(2x+3)*(x+2)}+\frac{2x^2+3x+8x+12}{(x+2)*(2x+3)}\)
\(\frac{x^2+11x+18}{(2x+3)*(x+2)}+\frac{2x^2+11x+12}{(x+2)*(2x+3)}\)
Now, we will add numerators as:
\(\frac{x^2+11x+18+2x^2+11x+12}{(2x+3)*(x+2)}\)
Combine like terms:
\(\frac{x^2+2x^2+11x+11x+18+12}{(2x+3)*(x+2)}\)
\(\frac{3x^2+22x+30}{(2x+3)*(x+2)}\)
Therefore, the simplified form of our given expression would be \(\frac{3x^2+22x+30}{(2x+3)*(x+2)}\).
