(-2)/(x-1)=(x-8)/(x+6)
To solve the equation (-2)/(x-1)=(x-8)/(x+6), we can start by cross multiplying.
Cross multiplying means multiplying the numerator of one side by the denominator of the other side.
On the left side, we have (-2) times (x+6), which gives us -2x-12.
On the right side, we have (x-8) times (x-1), which gives us x^2 - x - 8x + 8.
Now we have -2x-12 = x^2 - x - 8x + 8.
Next, we want to simplify the equation and bring all the terms to one side to solve for x.
First, let's combine like terms on the right side: -2x-12 = x^2 - 9x + 8.
Now, we can rearrange the equation to bring all the terms to one side: x^2 - 9x + 8 + 2x + 12 = 0.
Combine like terms to simplify further: x^2 - 7x + 20 = 0.
Now, we have a quadratic equation in the form ax^2 + bx + c = 0.
To solve this quadratic equation, we can use factoring, completing the square, or the quadratic formula.
In this case, the quadratic equation x^2 - 7x + 20 = 0 can be factored as (x-5)(x-4) = 0.
Setting each factor equal to zero, we have x-5 = 0 -> x = 5 and x-4 = 0 -> x = 4.
Therefore, the solutions to the equation (-2)/(x-1) = (x-8)/(x+6) are x = 5 and x = 4.