simplify -14x^3/x^3 -5x^4
A. -14/5x-1; where x ? 1/5, 0
B. -14x/1-5x ; where x ? 1/5
C. 1-5x/-14x ; where x ? 0
D. -14/1-5x; where x ? 1/5,0
Please use parentheses. I do not know what is the denominator.
-14x^3/x^3 -5x^4 = -14 - 5x^4
-14x^3/(x^3 -5x^4) = -14/(1-5x)
To simplify the expression (-14x^3/x^3) - 5x^4, we need to simplify the terms individually and then combine them.
First, let's simplify the first term, (-14x^3/x^3):
Since the variable x is in the numerator and the denominator with the same exponent, we can cancel out the x^3 terms:
(-14x^3/x^3) = -14
Next, let's simplify the second term, 5x^4:
There are no like terms to simplify, so we leave it as it is.
Now we can combine the simplified terms:
-14 - 5x^4
Therefore, the simplified expression is -14 - 5x^4.
None of the answer choices provided match the simplification we derived.
To simplify the expression (-14x^3)/(x^3 - 5x^4), we can factor out an x^3 from the numerator:
(-14x^3)/(x^3 - 5x^4) = (-14x^3)/(x^3(1 - 5x))
Now, we can cancel out the x^3 terms:
= -14/(1 - 5x)
So, the simplified expression is -14/(1 - 5x).
Now, let's go through the answer choices:
A. -14/5x-1 ; where x ? 1/5, 0
This answer choice is incorrect because it does not match the simplified expression we obtained.
B. -14x/1-5x ; where x ? 1/5
This answer choice is also incorrect because it does not match the simplified expression we obtained.
C. 1-5x/-14x ; where x ? 0
This answer choice is incorrect because it does not match the simplified expression we obtained.
D. -14/1-5x; where x ? 1/5,0
This answer choice is correct because it matches the simplified expression we obtained: -14/(1 - 5x). Additionally, the possible values of x are given as 1/5 and 0, which are valid solutions.
Therefore, the correct answer is D. -14/1-5x; where x ? 1/5, 0.