Solve for x and simplify the answer fully.

start fraction, x, minus, 1, divided by, x, plus, 1, end fraction, equals, start fraction, 9, divided by, 7, end fraction
x+1
x−1

=
7
9

1 answer

To solve the equation

\[ \frac{x - 1}{x + 1} = \frac{9}{7} \]

we can cross-multiply:

\[ 7(x - 1) = 9(x + 1). \]

Now, distribute both sides:

\[ 7x - 7 = 9x + 9. \]

Next, we will isolate \(x\) by moving all \(x\) terms to one side and constant terms to the other:

\[ 7x - 9x = 9 + 7, \] which simplifies to:

\[ -2x = 16. \]

Now, divide both sides by -2:

\[ x = -8. \]

Thus, the solution is

\[ \boxed{-8}. \]