Respuesta :
The expression which is equivalent to the difference of the given algebraic fraction is,
[tex]\dfr\dfrac{(x+5)(x+2)}{x(x-3)(x+3)}[/tex]
What is the difference?
Difference is the mathematical operation in which the one number is subtract from another number.
To find the difference of two fraction numbers, we find the least common factor of denominator and write the all numbers as one fraction.
The given expression in the problem is,
[tex]\dfrac{2x+5}{x^2-3x}-\dfrac{3x+5}{x^3-9x}-\dfrac{x+1}{x^2-9}[/tex]
Factorize the denominator of each term as,
[tex]\dfrac{2x+5}{x(x-3)}-\dfrac{3x+5}{x(x-3)(x+3)}-\dfrac{x+1}{(x-3)(x+3)}[/tex]
Here, the least common factor of the denominators is x(x-3)(x+3), therefore, the expression can be written as,
[tex]\dfrac{(x+3)(2x+5)-(3x+5)-(x)(x+1)}{x(x-3)(x+3)}\\\dfr\dfrac{2x^2+5x+6x+15-3x-5-x^2-x}{x(x-3)(x+3)}\\\dfr\dfrac{x^2+7x+10}{x(x-3)(x+3)}\\\dfr\dfrac{(x+5)(x+2)}{x(x-3)(x+3)}[/tex]
Hence, the expression which is equivalent to the difference of the given algebraic fraction is,
[tex]\dfr\dfrac{(x+5)(x+2)}{x(x-3)(x+3)}[/tex]
Learn more about the difference of two fractions here;
https://brainly.com/question/13222
