Evaluate the limit:lim𝑥→−5𝑥+5𝑥2−25=

To evaluate the limit of the function as x approaches -5, we first substitute -5 into the function:

(-5 + 5) / ((-5)^2 - 25)

This simplifies to:

0 / (25 - 25)

Which is 0/0, an indeterminate form.

However, we can simplify the function by factoring:

(x + 5) / (x^2 - 25)

The denominator is a difference of squares, so it can be factored as:

(x + 5) / ((x - 5)(x + 5))

The (x + 5) terms cancel out, leaving us with:

1 / (x - 5)

Now, we substitute -5 back into the simplified function:

1 / (-5 - 5)

Which simplifies to:

1 / -10

So, the limit of the function as x approaches -5 is -1/10.