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
B. -14x/1-5x where x = 1/5
To simplify the expression (-14x^3)/(x^3 - 5x^4), we can factor out an "x^3" from the numerator and the denominator:
(-14x^3)/(x^3 - 5x^4) = (-14x^3)/(x^3(1 - 5x))
Next, we can cancel out the common factor "x^3" from the numerator and the denominator:
(-14x^3)/(x^3(1 - 5x)) = -14/(1 - 5x)
Therefore, the simplified expression is -14/(1 - 5x).
However, none of the given answer choices match the simplified expression, so the correct answer choice is not provided.
To simplify the expression -14x^3 / (x^3 - 5x^4), we can first factor out the common term from the numerator and the denominator, which is x^3. This gives us:
-14x^3 / (x^3 - 5x^4) = -14x^3 / (x^3(1 - 5x))
Next, we can cancel out the x^3 term in the numerator and the denominator:
-14x^3 / (x^3(1 - 5x)) = -14 / (1 - 5x)
So, the simplified form of the expression is -14 / (1 - 5x).
To determine which option is the correct answer, let's evaluate the expression for the given values of x:
For x = 1/5:
-14 / (1 - 5x) = -14 / (1 - 5(1/5)) = -14 / (1 - 1) = -14 / 0
Since dividing by 0 is undefined, the expression is undefined when x = 1/5.
For x = 0:
-14 / (1 - 5x) = -14 / (1 - 5(0)) = -14 / (1 - 0) = -14 / 1 = -14
Therefore, the correct answer is option:
D. -14/1-5x where x = 1/5, 0