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? (6 points)

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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? (6 points)

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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]

I did the work on a platform that would let me add the "______" so ya sorry if its small but i hope i helped.

[tex]What is the least common denominator of the fraction 2 over x plus the fraction x over x plus 1 plus[/tex]

We need to know what x is

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

3x is the least common denominators because you need to be able to make sure all other denominators can go multiple into it. Since the rest are just x, the largest number of 3x would be the denominator you want.