Answer
$x=\dfrac{-5}{9}$
Work Step by Step
We are given that $9=\dfrac{4}{1+x}$
Re-arrange as: $4=9(1+x)$
or, $9x+9-4=0$
This gives $9x+5=0 \implies x=\dfrac{-5}{9}$
We need to check the solution.
$9=\dfrac{4}{1+(\dfrac{-5}{9})}$
or, $9=\dfrac{4}{1-\dfrac{-5}{9}}$
or, $9=9$ Verified.
