To solve the equation
[tex]\(\frac{x-3}{x-5} = (x+1)(x+6)\)[/tex],
the first step is to eliminate the denominator on the left side of the equation. This can be done by multiplying both sides of the equation by [tex]\((x-5)\)[/tex]:
[tex]\[
(x-5) \cdot \frac{x-3}{x-5} = (x-5) \cdot (x+1)(x+6)
\][/tex]
When you multiply both sides by [tex]\((x-5)\)[/tex], it cancels out the denominator on the left side of the equation:
[tex]\[
x-3 = (x-5)(x+1)(x+6)
\][/tex]
So, to fill in the blank, the first step in solving [tex]\(\frac{x-3}{x-5} = (x+1)(x+6)\)[/tex] is to multiply both sides by [tex]\((x-5)\)[/tex].
