Final answer:
To find the sum in simplest form, find a common denominator which is (x-5)², then combine the fractions, resulting in the sum being (6x² - 30x + 6) / (x-5)².
Step-by-step explanation:
The student is asking to find the sum of the given expressions 6x/(x-5) and 6/(x-5)² in simplest form. To combine these into a single fraction, we need a common denominator. The common denominator in this case would be (x-5)². Following the method to simplify the expression, we can rewrite the sum as follows:
- For the first term 6x/(x-5), we already have x-5 in the denominator, so we need to multiply the numerator and denominator by x-5 to get the common denominator of (x-5)².
- For the second term 6/(x-5)², the denominator is already (x-5)², so we can leave it as it is.
The expressions will look like this:
- 6x/(x-5) becomes 6x(x-5)/(x-5)²
- 6/(x-5)² remains unchanged.
Now, we can add the two fractions since they have the same denominator:
[6x(x-5) + 6] / (x-5)² = (6x² - 30x + 6) / (x-5)²
This is the simplified form of the given sum.