Simplify. 5 times x cubed over the quantity 7 times x cubed plus x to the fourth power
A. 5 over the quantity 7 plus x, where x does not equal 0, negative 7
B. 5 over the quantity 7 plus x, where x does not equal negative 7
C. 5 over 7 times x, where x does not equal 0
D. five sevenths
B. 5 over the quantity 7 plus x, where x does not equal negative 7
To simplify the expression 5 times x cubed over the quantity 7 times x cubed plus x to the fourth power, the first step is to factor out the common factors in both the numerator and denominator.
The expression can be rewritten as 5x^3 / (7x^3 + x^4).
Next, try to simplify further by factoring out an x^3 from both terms in the denominator:
5x^3 / (x^3 * (7 + x)).
Now, the x^3 terms cancel out, leaving:
5 / (7 + x).
Therefore, the simplified expression is 5 over the quantity 7 plus x, where x does not equal 0 or negative 7.
So, the correct answer is option B: 5 over the quantity 7 plus x, where x does not equal negative 7.