Answer:
The least common denominator of the fraction is:
3x(x − 1)
Step-by-step explanation:
We are given a algebraic expression in terms of the variable x as follows:
The fraction 7 over 3 x plus the fraction 2 over x plus the fraction x over x minus 1.
Mathematically it is expressed as follows:
[tex]=\dfrac{7}{3x}+\dfrac{2}{x}+\dfrac{x}{x-1}[/tex]
Hence, on taking the Least common Multiple we get:
[tex]=\dfrac{7(x-1)+2\times 3(x-1)+x\times 3x}{3x(x-1)}[/tex]
which is given by:
[tex]=\dfrac{7x-7+6x-6+3x^2}{3x(x-1)}\\\\\\=\dfrac{3x^2+13x-13}{3x(x-1)}[/tex]
Hence, the answer is:
3x(x-1)
