Question

This is solving rational equationsI really need some help. Please explain how you get each step if u can.

Answer 1

We are given the following equation:

`(-4)/(x+4)=-(3)/(x+6)`

we are asked to determine any extraneous solutions. To do that we will determine the values of "x" that solve the equation. First, we will cross multiply the equation:

`-4(x+6)=-3(x+4)`

Now, we can multiply by -1, we get:

`4(x+6)=3(x+4)`

Now we use the distributive property on both sides, we get:

`4x+24=3x+12`

Now, we subtract "3x" from both sides:

`\begin{gathered} 4x-3x+24=3x-3x+12 \\ x+24=12 \end{gathered}`

Now we subtract 24 from both sides:

`\begin{gathered} x+24-24=12-24 \\ x=-12 \end{gathered}`

Therefore, the solution is x = -12. The extraneous solutions are the solutions that are not in the domain of the original function.

In the domain of the original function, we have that the values of:

`\begin{gathered} x=-4 \\ x=-6 \end{gathered}`

Would make the denominators equal to zero, and therefore, they are not in the domain. Since the solution is none of these values there are no extraneous solutions.