(-2)/(x-1)=(x-8)/(x+6)
please help me with this
"cross-multiply"
(x-1)(x-8) = -2(x+6)
expand and solve as a quadratic
is 7/8 the answer for this
No,
x^2 - 9x + 8 = -2x - 12
x^2 - 7x + 20 = 0
Using the quadratice formula I got
imaginary roots of
(7 ±i√31)/2
To solve the equation (-2)/(x-1) = (x-8)/(x+6), we need to get rid of the fractions and find the value of x that satisfies the equation.
Here's the step-by-step solution:
Step 1: Multiply both sides of the equation by (x-1) and (x+6) to eliminate the denominators:
(x-1) * ((-2)/(x-1)) = (x-1) * ((x-8)/(x+6))
(x+6) * ((x-8)/(x+6)) = (x+6) * ((-2)/(x-1))
Simplifying these expressions, we get:
-2 = (x-8)*(x+6)
(x-8)*(x+6) = -2
Step 2: Expand and simplify the equations:
-2 = x^2 - 8x + 6x - 48
x^2 - 2x - 46 = 0
Step 3: Rearrange the equation in standard quadratic form:
x^2 - 2x - 46 = 0
Step 4: Factor or use the quadratic formula to solve for x.
Unfortunately, this equation cannot be factored easily. So we'll use the quadratic formula to find the solutions:
x = (-b ± √(b^2 - 4ac)) / 2a
For the equation x^2 - 2x - 46 = 0, a = 1, b = -2, and c = -46.
x = (-(-2) ± √((-2)^2 - 4*1*(-46))) / (2*1)
x = (2 ± √(4 + 184)) / 2
x = (2 ± √188) / 2
x = (2 ± 2√47) / 2
x = 1 ± √47
Therefore, the solutions to the equation are x = 1 + √47 and x = 1 - √47.