Answer:
The least common denominator of the given rational expression is (x-3).
Step-by-step explanation:
A fraction is made up of two integers.
The top number in a fraction is known as numerator of the fraction.
The bottom number in a fraction is known as denominator of the fraction.
To find least common denominator, first we need to find out prime factors of the denominator of each fraction.
Given expression is:
[tex]\frac{2}{x^2-3x}+\frac{5}{x^2+x-12}[/tex]
[tex]\therefore \frac{2}{x^2-3x}[/tex]
[tex]=\frac{2}{x(x-3)}[/tex] [ Taking common x]
[tex]\therefore\frac{5}{x^2+x-12}[/tex]
[tex]=\frac{5}{x^2+4x-3x-12}[/tex] [ applying factorizing method, spiting 1x = 4x-3x in such way that (4)×(-3) = -12]
[tex]=\frac{5}{x(x+4)-3(x+4)}[/tex]
[tex]=\frac{5}{(x+4)(x-3)}[/tex]
The least common denominator of the rational expression is (x-3).
