Question

Simplify and select the answer with the appropriate restrictions for the variables.

5x-3x^2/2x^4



A. 1/2




B.1/2, (x≠0




C.5-3x/2x^3, (x≠0)




D.5/2x^2,(x≠0)

Answer 1

The expression simplifies to (5-3x)/2x^3 with the restriction that x cannot be zero. This is because we cannot divide by zero. Option C is the correct answer.

Step-by-step explanation:

To simplify the given expression 5x-3x^2/2x^4, we need to factor out an x from the numerator and then reduce the fraction by canceling out terms that appear both in the numerator and the denominator.

Here is the step-by-step simplification:

1. Factor x from the numerator: x(5-3x)/2x^4.
2. Cancel x from the numerator and one x from the denominator: (5-3x)/2x^3.
3. As a result, the simplified form is (5-3x)/2x^3.

The restriction for the variable x is that x≠0 because division by zero is undefined.

So, the correct answer to the question, with the appropriate restrictions, is option C: 5-3x/2x^3, (x≠0).

Answer 2

5x-3x^2/2x^4 =x(5-3x) / 2x.(x^3), simplified by x, we have 5-3x/2x^3, (x≠0)
so the answer is C.5-3x/2x^3, (x≠0)