Answer:
the simplified expression is [tex]\frac{x+4}{5}[/tex]
Step-by-step explanation:
Given;
[tex]\frac{x^2 + 6x + 2}{5x + 15} + \frac{x+ 10}{5x+ 15}[/tex]
1. Rewrite the expression as a single fraction as follows;
[tex]\frac{x^2 + 6x + 2}{5x + 15} + \frac{x+ 10}{5x+ 15} = \frac{x^2 + 6x + 2 \ + \ {x+ 10} }{5x + 15} = \frac{x^2 + 7x + 12}{5x + 15}[/tex]
2. By combining like terms we had [tex]\frac{x^2 + 7x + 12}{5x + 15}[/tex]
3. The expression is simplified as follows;
Factorize the numerator and denominator;
[tex]\frac{x^2 + 7x + 12}{5x + 15} = \frac{x^2 + 3x + 4x + 12}{5(x + 3)} = \frac{x(x + 3) + 4(x + 3)}{5(x + 3)} = \frac{(x + 3)(x + 4)}{5(x + 3)} = \frac{x + 4}{5}[/tex]
Therefore, the simplified expression is [tex]\frac{x+4}{5}[/tex]
