Question

Solving for x gives us x = ?The value for x cannot equal ?

Answer 1

Solving the rational equation, we have:

`\begin{gathered} (5)/(x+1)+(1)/(x-3)=(-6)/(x^2-2x-3) \\ (5(x-3)+1(x+1))/((x+1)(x-3))=(-6)/((x+1)(x-3)) \\ 5x-15+x+1=-6 \\ 6x-14=-6 \\ 6x=-6+14 \\ 6x=8 \\ x=(8)/(6)=(4)/(3) \end{gathered}`

So the solution is x = 4/3 = 1.33

Now let's calculate the values that x cannot be equal, calculating where the denominators of the fractions are equal to zero:

`\begin{gathered} x+1\\e0\to x\\e-1 \\ x-3\\e0\to x\\e3 \end{gathered}`

So x cannot be equal to -1 or 3.