Question

91 pointSimplify the following function4.222-25 12-36O4(x+6(22-25)(4x+6)+ +5,0(x+5)(8-5) 2 + +6, +5,0O4(x+6)(3-5)(x+5)*7 +5, +6,0(2+5)27-5,0O

Answer 1

`\begin{gathered} -(4(x+6))/((x-5)(x+5)) \\ x\\e\pm5,\pm6,0 \end{gathered}`

Step-by-step explanation

We want to simplify the expression:

`-(4x)/(x^2-25)/((x^2-6x))/(x^2-36)`

To do this, first change the sign to a multiplication sign and flip the fraction on the right:

`-(4x)/(x^2-25)\cdot(x^2-36)/((x^2-6x))`

Now, simplify the expression by applying the difference of two squares and factorization:

`\begin{gathered} -(4x)/((x-5)(x+5))\cdot((x-6)(x+6))/(x(x-6)) \\ \Rightarrow-(4)/((x-5)(x+5))\cdot((x+6))/(1) \\ \Rightarrow-(4(x+6))/((x-5)(x+5)) \end{gathered}`

The expression will be invalid when x is:

`\pm5,\pm6,0`

Therefore, the answer is option C.