Question

What is the least common denominator of the fraction 2 over x plus the fraction x over x plus 1 plus the fraction x plus 1 over 3 x

Answer 1

Answer:

The least common denominator is  $3x^2+3x$ .

Step-by-step explanation:

Given : Expression $\frac{2}{x}+ \frac{x}{x+1}+\frac{x+1}{3x}$

To find : What is the least common denominator of the given expression?

Solution :

Least common denominator is the common factor in the denominator.

Expression $\frac{2}{x}+ \frac{x}{x+1}+\frac{x+1}{3x}$

Since, The least common factor in x,(x+1),3x is $3x(x+1)=3x^2+3x$

Now, If we take least common multiple,

$=\frac{2(3(x+1))+x(3x)+(x+1)(x+1)}{3x(x+1)}$

$=\frac{4x^2+8x+7}{3x^2+3x}$

Here, $4x^2+8x+7$ is the numerator and  $3x^2+3x$ is the denominator.

Therefore,The least common denominator is  $3x^2+3x$

Answer 2

LCD: 3X(X+1). Has the x+1,x, and 3x which consists of each of the denominatiors.