Question

Find the difference. Express your answer in simplest form.

4s/s2 – 10s + 25
20/s2-10s + 25
a. 1/5s-5 b. 2/5s-5 c. 1/s-5 d. 1/5s-10

Answer 1

The difference of the two expressions is 4/(s - 5), which is obtained by subtracting the second expression from the first and simplifying. The answer none of the provided options match, indicating there might be a mistake in the provided options.

Step-by-step explanation:

The student asked to find the difference and express the answer in simplest form given the expressions 4s/s2 – 10s + 25 and 20/s2-10s + 25. To find the difference between the two expressions, we need to subtract the second expression from the first:

4s/(s2 – 10s + 25) - 20/(s2 - 10s + 25)

Both expressions have the same denominator, so we can combine them directly:

(4s - 20) / (s2 - 10s + 25)

Simplifying the numerator gives us:

(4s - 20) / (s2 - 10s + 25) = 4(s - 5) / (s2 - 10s + 25)

Factor out 4 from the numerator:

4(s - 5) / [(s - 5)(s - 5)]

Now, notice that (s - 5) is a common factor in both the numerator and the denominator, which means they can cancel each other out. So, the simplified form is:

4 / (s - 5)

None of the options provided by the student matches this result, so there may be a mistake in the provided options or in the interpretation of the expressions. It is important to read the original problem carefully to ensure there are no typos or mistakes.