Question

Needing help understanding how to solve these math problems

Answer 1

We have the following:

The first thing is to simplify the expression as much as possible.

In the case of the vertical asymptote: The values that x cannot take is when it makes the denominator zero, therefore we must set the denominator equal to 0 and thus calculate the value of x that will make the function undefined.

2.

`\begin{gathered} (4x^6)/(2x-6)=(2\cdot2x^6)/(2(x-3))=(2x^6)/((x-3)) \\ x-3=0 \\ x=3 \end{gathered}`

3.

`\begin{gathered} (6x^2+13x-5)/(6x^2-23x+7)=((3x-1)(2x+5))/((3x-1)(2x-7))=(2x+5)/(2x-7) \\ 2x-7=0 \\ x=(7)/(2) \end{gathered}`

4.

`\begin{gathered} (x+4)/(3x^2+11x-4)=(x+4)/((3x-1)(x+4))=(1)/(3x-1) \\ 3x-1=0 \\ x=(1)/(3) \end{gathered}`

5.

`\begin{gathered} (-x-4)/(x^2-x-20)=(-(x+4))/((x+4)(x-5))=(-1)/(x-5) \\ x-5=0 \\ x=5 \end{gathered}`

6.