Question

Solve the rational equation, State the excluded values -2/x-8 = x-1/x+2

Answer 1

Answer::

`\begin{gathered} x=3\text{ or 4} \\ x\\eq8,x\\eq-2 \end{gathered}`

Step-by-step explanation:

Given the rational function:

`(-2)/(x-8)=(x-1)/(x+2)`

Step 1: Cross-multiply

`-2(x+2)=(x-1)(x-8)`

Step 2: Expand and simplify

`\begin{gathered} -2x-4=x^2-8x-x+8 \\ -2x-4=x^2-9x+8 \\ x^2-9x+2x+8+4=0 \\ x^2-7x+12=0 \end{gathered}`

Step 3: Solve the quadratic equation for x.

`\begin{gathered} x^2-7x+12=0 \\ x^2-4x-3x+12=0 \\ x(x-4)-3(x-4)=0 \\ (x-3)(x-4)=0 \\ x-3=0\text{ or }x-4=0 \\ x=3\text{ or }x=4 \end{gathered}`

Step 4: Find the excluded values

The excluded values are the values at which the function is undefined.

Set the denominators equal to zero.

`\begin{gathered} x-8=0\text{ or x+2=0} \\ x=8,x=-2 \end{gathered}`

Thus the solution of the function is:

`\begin{gathered} x=3\text{ or 4} \\ x\\eq8,x\\eq-2 \end{gathered}`