Question

Thank you If you helped
Identify all values of that make the equation true: x-3/x = -8/x+3

Answer 1

x = - 9 , x = 1

Explanation:

given

`(x-3)/(x)` =
`(-8)/(x+3)` ( cross- multiply )

(x - 3)(x + 3) = - 8x ← expand left side using FOIL

x² - 9 = - 8x ( add 8x to both sides )

x² + 8x - 9 = 0 ← quadratic equation in standard form

(x + 9)(x - 1) = 0 ← in factored form

equate each factor to zero and solve for x

x + 9 = 0 ⇒ x = - 9

x - 1 = 0 ⇒ x = 1

the solutions to the equation are x = - 9 and x = 1