Multiply the argument of the limit by the conjugate.

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Apply the distributive property.

Apply the distributive property.

Apply the distributive property.

Reorder the factors in the terms and .

Add and .

Add and .

Multiply by .

Rewrite using the commutative property of multiplication.

Multiply .

Raise to the power of .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Rewrite as .

Use to rewrite as .

Apply the power rule and multiply exponents, .

Combine and .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Simplify.

Apply the distributive property.

Multiply by .

Move to the left of .

Apply the distributive property.

Multiply by .

Subtract from .

Subtract from .

The limit at negative infinity of a polynomial of odd degree whose leading coefficient is negative is infinity.

Evaluate limit as x approaches negative infinity of x+ square root of x^2+6x