Answer:
[tex]\frac{2(x^{2} + 5x + 3)}{(x+3)(x+5)}[/tex]
Step-by-step explanation:
We need to sum the following two expressions:
[tex]\frac{x}{x+3} + \frac{x+2}{x+5}[/tex]
[tex]\frac{x(x+5) + (x+2)(x+3)}{(x+3)(x+5)}[/tex]
expanding the polynomial in the numerator:
[tex]\frac{2x^{2} + 10x + 6}{(x+3)(x+5)}[/tex]
[tex]\frac{2(x^{2} + 5x + 3)}{(x+3)(x+5)}[/tex]
This is the most simplified form we can get:
[tex]\frac{2(x^{2} + 5x + 3)}{(x+3)(x+5)}[/tex]
Answer:
[tex]\frac{2(x^{2}+5x+3)}{(x+3)(x+5)}[/tex]
Step-by-step explanation:
The given expression is [tex]\frac{x}{x+3}+\frac{x+2}{x+5}[/tex]
We have to simplify the given expression
[tex]\frac{x}{x+3}+\frac{x+2}{x+5}[/tex]
= [tex]\frac{x(x+5)+(x+2)(x+3)}{(x+3)(x+5)}[/tex] [Distributive law]
= [tex]\frac{x^{2}+5x+x^{2}+3x+2x+6}{(x+3)(x+5)}[/tex]
= [tex]\frac{2x^{2}+10x+6}{(x+3)(x+5)}[/tex]
= [tex]\frac{2(x^{2}+5x+3)}{(x+3)(x+5)}[/tex]
Finally the simplified form of the given expression is [tex]\frac{2(x^{2}+5x+3)}{(x+3)(x+5)}[/tex]
