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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

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LCD: 3X(X+1). Has the x+1,x, and 3x which consists of each of the denominatiors.
User Charlotta
by
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4 votes

Answer:

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

User TomNg
by
8.4k points

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