Respuesta :
Answer:
[tex]\frac{5(x-1)}{3x}[/tex]
Step-by-step explanation:
The given expression is
[tex]\frac{5x^{2} -5}{3x^{2}+3x}[/tex]
To simplify this rational expression, we need to extract the greatest common factor of each part,
[tex]\frac{5x^{2} -5}{3x^{2}+3x}=\frac{5(x^{2}-1) }{3x(x+1)}[/tex]
Then, we observe that the numerator has a difference of two perfect squares, which can be factored as
[tex]a^{2} -b^{2} =(a-b)(a+b)[/tex]
Where, [tex]a=x[/tex] and [tex]b=1[/tex]
[tex]x^{2} -1=(x-1)(x+1)[/tex]
Now, we applied this to the rational expression
[tex]\frac{5x^{2} -5}{3x^{2}+3x}=\frac{5(x^{2}-1) }{3x(x+1)}=\frac{5(x-1)(x+1)}{3x(x+1)}=\frac{5(x-1)}{3x}[/tex]
Therefore the simplified form of the given expression is
[tex]\frac{5(x-1)}{3x}[/tex]
