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

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

Answer 2

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

Explanation:

Given : Expression
`(2)/(x)+ (x)/(x+1)+(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
`(2)/(x)+ (x)/(x+1)+(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,

`=(2(3(x+1))+x(3x)+(x+1)(x+1))/(3x(x+1))`

`=(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`