Answer:
D) The given expression [tex](\frac{3x}{x+ 3}) + (\frac{x+2}{x}) = \frac{4x^{2} + 5x + 6}{(x+3)(x)}[/tex]
Step-by-step explanation:
Here, the given expression is : [tex](\frac{3x}{x+ 3}) + (\frac{x+2}{x})[/tex]
Let us simplify the given expression be taking LCM of the denominator and making a common base denominator.
We get : [tex](\frac{3x}{x+ 3}) + (\frac{x+2}{x}) = \frac{3x(x) + (x+2)(x+3)}{(x+3)(x)} \\\implies\frac{3x^{2} + (x+2)(x+3)}{(x+3)(x)}[/tex]
Solving [tex](x+2) (x+3) = x^{2} + 2x + 3x + (2)(3) = x^{2} + 5x + 6[/tex]
Now, substitute the above value into the given expression :
[tex]\frac{3x^{2} + (x+2)(x+3)}{(x+3)(x)} \implies\frac{3x^{2} + x^{2} + 5x + 6}{(x+3)(x)}\\= \frac{4x^{2} + 5x + 6}{(x+3)(x)}[/tex]
Hence, the given expression [tex](\frac{3x}{x+ 3}) + (\frac{x+2}{x}) = \frac{4x^{2} + 5x + 6}{(x+3)(x)}[/tex]
Answer:
The correct answer is [tex]\frac{4x^2+5x+6}{x(x+3)}[/tex]
Step-by-step explanation:
I took the quiz! I hope this helps! :)
(btw, if anyone ever gives you links, don't click on them, they're viruses)
