Can someone check a few answers for me? Thank you.

1. Simplify. (-14x^3) / (x^3) - (5x^4)
= -14/1-5x Where x is not equal to 1/5, 0
2. Simplify. x - 2 / (x^2) + (4x) - 12
= 1/x+6 Where x is not equal to -6

THe first one is good.

But on the second one you forgot the other restriction. You need to set your restrictions-before you reduce. You reduced the x-2 but forgot to set x-2 not equal to 0 for the final restriction : )

Thank you very much!

To verify the answers, let's simplify the expressions step by step and compare them with your provided answers.

1. Simplify: (-14x^3) / (x^3) - (5x^4)
To simplify this expression, we'll divide the numerator by the denominator and then subtract the second term.

(-14x^3) / (x^3) - (5x^4) = -14/1 - 5x
This step is incorrect because when dividing like terms with exponents, we subtract the exponents.

The correct simplification would be:
(-14x^3) / (x^3) - (5x^4) = -14 - 5x^(4-3) [using the rule x^a/x^b = x^(a-b)]
= -14 - 5x
Therefore, the correct simplification of (-14x^3) / (x^3) - (5x^4) is -14 - 5x.

2. Simplify: x - 2 / (x^2) + (4x) - 12
To simplify this expression, we'll combine like terms in the numerator and denominator.

x - 2 / (x^2) + (4x) - 12 = (x - 2) / (x^2 + 4x - 12)

This step is correct. The expression x - 2 / (x^2) + (4x) - 12 simplifies to (x - 2) / (x^2 + 4x - 12).

Now, let's compare the simplified expressions with your provided answers:

1. Simplify. (-14x^3) / (x^3) - (5x^4)
Your answer: -14/1-5x

Correct answer: -14 - 5x

The provided answer is incorrect as the terms and parentheses are not placed correctly.

2. Simplify. x - 2 / (x^2) + (4x) - 12
Your answer: 1/x+6

Correct answer: (x - 2) / (x^2 + 4x - 12)

The provided answer matches the correct simplification, where x is not equal to -6.

Please double-check your calculations and make the necessary adjustments accordingly.