(х+3)^-2(х+3)-8=0

To solve the equation \((x+3)^{-2}(x+3) - 8 = 0\), we can first simplify the expression. 1. Simplify the term \((x+3)^{-2}(x+3)\): \[ (x+3)^{-2}(x+3) = (x+3)^{-1} = \frac{1}{x+3} \] 2. So, the equation becomes: \[ \frac{1}{x+3} - 8 = 0 \] 3. To isolate the fractional term, we can add 8 to both sides: \[ \frac{1}{x+3} = 8 \] 4. Next, we can cross-multiply to solve for \(x\): \[ 1 = 8(x+3) \] 5. Expand the right side: \[ 1 = 8x + 24 \] 6. Subtract 24 from both sides: \[ 1 - 24 = 8x \] \[ -23 = 8x \] 7. Divide both sides by 8 to solve for \(x\): \[ x = -\frac{23}{8} \] Thus, the solution to the equation is: \[ \boxed{-\frac{23}{8}} \]