Answer:
The least common denominator is [tex]3x^2+3x[/tex] .
Step-by-step explanation:
Given : Expression [tex]\frac{2}{x}+ \frac{x}{x+1}+\frac{x+1}{3x}[/tex]
To find : What is the least common denominator of the given expression?
Solution :
Least common denominator is the common factor in the denominator.
Expression [tex]\frac{2}{x}+ \frac{x}{x+1}+\frac{x+1}{3x}[/tex]
Since, The least common factor in x,(x+1),3x is [tex]3x(x+1)=3x^2+3x[/tex]
Now, If we take least common multiple,
[tex]=\frac{2(3(x+1))+x(3x)+(x+1)(x+1)}{3x(x+1)}[/tex]
[tex]=\frac{4x^2+8x+7}{3x^2+3x}[/tex]
Here, [tex]4x^2+8x+7[/tex] is the numerator and [tex]3x^2+3x[/tex] is the denominator.
Therefore,The least common denominator is [tex]3x^2+3x[/tex]
