- #1
elsacozine
- 4
- 0
(k + 7/k^2 + 6K + 9) + (k - 5/k^2 - 5k - 24)
suluclac said:Both denominators should factor nicely.
Although true, is it really relevant to finding the sum?
greg1313 said:Hi elsacozine and welcome to MHB! :D
Do you mean "Find the sum:
$$\dfrac{k + 7}{k^2 + 6k + 9} + \dfrac{k - 5}{k^2 - 5k - 24}$$
?
elsacozine said:Yes; I meant that. Sorry I didn't know how to write it like that.
MarkFL said:Okay, so what you want to do is first factor the two denominators (if possible), so that you can determine the LCD. What do you get when factoring?
elsacozine said:when i factor it i get:
(k + 7)/(k + 3)(k + 3) + (k - 5)/(k - 8)(k + 3)
MarkFL said:Yes, and we can write this as:
\(\displaystyle \frac{k+7}{(k+3)^2}+\frac{k-5}{(k-8)(k+3)}\)
So, what is our LCD?
elsacozine said:the LCD is (k - 8)(k + 3)^2...
so would you multiply the fractions by the their missing factors. then the denominators should be the same (LCD), then you could add the two fractions because they have common denominators?
To simplify this expression, we first need to combine like terms. This involves adding or subtracting the coefficients of terms with the same variable and exponent. In this case, the terms (k + 7) and (k) both have a k term, so we can combine them to get (2k + 7). Similarly, the terms (k^2 + 6k) and (k^2 - 5k) can be combined to get (2k^2 + k). Finally, the terms (9) and (-24) can be combined to get (-15). This gives us the simplified expression of (2k^2 + 3k - 15).
No, the expression cannot be further simplified as we have combined all like terms and there are no common factors that can be factored out.
To add or subtract fractions with variables in the denominator, we first need to find a common denominator. In this case, we can multiply the first fraction (k + 7/k^2 + 6K + 9) by (k - 5)/(k - 5) to get a common denominator of (k^2 + k - 63). This gives us the new expression of (k^2 + k - 63 + k^2 - 5k + 35)/(k^2 + k - 63). We can then combine like terms to get the simplified expression of (2k^2 - 4k - 28)/(k^2 + k - 63).
Yes, the expression can be written as a single fraction by finding a common denominator and combining the fractions. As shown in the previous question, the common denominator is (k^2 + k - 63). Combining the fractions gives us the expression of (2k^2 - 4k - 28)/(k^2 + k - 63).
Simplifying expressions allows us to better understand and analyze mathematical relationships in scientific experiments and theories. It can also help us solve complex equations and make predictions based on mathematical models. In the context of this specific expression, simplifying it can allow us to see the relationship between different variables and possibly make further simplifications or substitutions to better understand the underlying scientific concept.