The least common denominator for the function [tex]\frac{11x}{x^{2} +4x-12} -\frac{7}{2x^{2} -4x}[/tex] is (x -2).
What is least common denominator?
The least common multiple of a group of fractions' denominators is known as the lowest common denominator, or Least Common Denominator.
Calculation for the least common denominator:
Consider the given expression,
[tex]\frac{11x}{x^{2} +4x-12} -\frac{7}{2x^{2} -4x}[/tex]
Further simplifying the equation by factorisation of the denominator part
= [tex]\frac{11x}{x^{2} +6x-2x-12} -\frac{7}{2x(x -2)}[/tex]
= [tex]\frac{11x}{(x+6)(x-2)} -\frac{7}{2x(x -2)}[/tex]
= [tex]\frac{1}{x-2}[/tex]×[tex][\frac{11x}{(x+6)} -\frac{7}{2x}][/tex]
Therefore, from the above result, it is found that (x-2) is the least common denominator that can be taken.
To know more about factorisation, here
https://brainly.com/question/10718512
#SPJ2
