Answer:
C: \(\frac{x-1}{x+3}\)
Step-by-step explanation:
The simplest form of the expression below, can be found through factorization process.
\(\frac{x^{2}+5x-6}{x^{2}+9x+18}\)
We have two quadratic expression. To find their factor, we only need to apply some steps:
Factorizing \(x^{2}+5x-6=(x+a)(x-b)\)
We have to find to numbers a and b that multiplied result in 6, but subtracted result in 5. We can see that \(a = 6\) and \(b=1\) are the right numbers, because 6 times 1 equals 6, and 6 minus 1 equals 5.
Therefore, \(x^{2}+5x-6=(x+6)(x-1)\)
On the other expression, we applied the same process:
\(x^{2}+9x+18=(x+6)(x+3)\); because, \(6(3)=18\) and \(6+3=9\)
Then, we replace these factors for each expression:
\(\frac{x^{2}+5x-6}{x^{2}+9x+18}\)
\(\frac{(x+6)(x-1)}{(x+6)(x+3)}\)
Eliminating similar factors, we have:
\(\frac{(x-1)}{(x+3)}\)
Which is the simples form.