Answer :

Let's solve the equation [tex]\(\frac{54}{h-1} = 3\)[/tex] step-by-step.

1. Remove the denominator:
To eliminate the fraction, multiply both sides of the equation by [tex]\((h - 1)\)[/tex]:
[tex]\[ 54 = 3 \cdot (h - 1) \][/tex]

2. Distribute the 3 on the right side:
Now distribute the [tex]\(3\)[/tex] inside the parenthesis:
[tex]\[ 54 = 3h - 3 \][/tex]

3. Isolate the term with [tex]\(h\)[/tex]:
Add [tex]\(3\)[/tex] to both sides of the equation to move the constant term:
[tex]\[ 54 + 3 = 3h \][/tex]
Simplify it:
[tex]\[ 57 = 3h \][/tex]

4. Solve for [tex]\(h\)[/tex]:
To isolate [tex]\(h\)[/tex], divide both sides of the equation by [tex]\(3\)[/tex]:
[tex]\[ h = \frac{57}{3} \][/tex]
Simplify it:
[tex]\[ h = 19 \][/tex]

Thus, the value of [tex]\(h\)[/tex] is [tex]\(19\)[/tex].