Answer: The correct option is (c) \(\dfrac{(x-1)}{(x+3)}.\)
Step-by-step explanation: The given expression to simplify is
\(E=\dfrac{x^2+5x-6}{x^2+9x+18}.\)
To simplify the above expression, at first we will try to factorise both the number and denominator into linear factors. Then, we will cancel the common factors, if exists.
The simplification is as follows:
\(E\\\\\\=\dfrac{x^2+5x-6}{x^2+9x+18}\\\\\\=\dfrac{x^2+6x-x-6}{x^2+6x+3x+18}\\\\\\=\dfrac{x(x+6)-1(x+6)}{x(x+6)+3(x+6)}\\\\\\=\dfrac{(x+6)(x-1)}{(x+6)(x+3)}\\\\\\=\dfrac{(x-1)}{(x+3)}.\)
Thus, the correct simplified form is (c). \(\dfrac{(x-1)}{(x+3)}.\)
