Respuesta :
Answer:
[tex]\frac{(x+5)(x+2)}{x(x-3)(x+3)}[/tex]
Step-by-step explanation:
The given expression is
[tex]\frac{2x+5}{x^{2} -3x} -\frac{3x+5}{x^{3} -9x} -\frac{x+1}{x^{2}-9}[/tex]
First, we need to factor each denominator
[tex]\frac{2x+5}{x(x-3)} -\frac{3x+5}{x(x+3)(x-3)} -\frac{x+1}{(x-3)(x+3)}[/tex]
So, the least common factor (LCF) is [tex]x(x-3)(x+3)[/tex], because they are the factors that repeats.
Now, we diviide the LCF by each denominator, to then multiply it by each numerator.
[tex]\frac{(x+3)(2x+5)-3x-5-x(x+1)}{x(x-3)(x+3)} =\frac{2x^{2}+5x+6x+15-3x-5-x^{2}-x }{x(x-3)(x+3)}\\\frac{x^{2}+7x+10}{x(x-3)(x+3)}[/tex]
Then, we factor the numerator, to do so, we need to find two numbers which product is 10 and which sum is 7.
[tex]\frac{(x+5)(x+2)}{x(x-3)(x+3)}[/tex]
Therefore, the expression is equivalent to
[tex]\frac{(x+5)(x+2)}{x(x-3)(x+3)}[/tex]
