Answer
$-1$
Work Step by Step
When we multiply the numerator and denominator of a rational expression with a nonzero expression,
we are multiplying the rational expression with 1.
Multiplying with 1 does not change the value, so the resulting rational expression is equivalent to the initial one..
Here, we have: initial rational expression = $\displaystyle \frac{7}{(9-5x)}$.
Multiply it with $1=\displaystyle \frac{A}{A}$, where A is some nonzero expression:
$\displaystyle \frac{7}{(9-5x)}\cdot\frac{A}{A}=\frac{7\cdot A}{(9-5x)\cdot A}$
We want the resulting denominator to be $5x-9.$
$5x-9=-(9-5x)=(9-5x)(-1)$
so, we see that $A=-1.$
