Question

What is the simplified form of the quantity of x plus 9, all over the quantity of 2x plus 3 + the quantity of x plus 4, all over the quantity of x plus 2?

Answer 1

$\frac{x+9}{2x+3} + \frac{x+4}{x+2} \\ = \frac{(x+9)(x+2)+(x+4)(2x+3)}{(2x+3)(x+2)} \\ = \frac{ x^{2} +11x+18+2 x^{2} +11x+12}{(2x+3)(x+2)} \\ \frac{3 x^{2} +22x+30}{(2x+3)(x+2)}$

Answer 2

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 $\frac{3x^2+22x+30}{(2x+3)*(x+2)}$.