Answer: OPTION A.
Step-by-step explanation:
Given the equation [tex]\frac{c-1}{x}+d=cd[/tex], you need to solve for the variable "x":
Subtract "d" from both sides of the equation:
[tex]\frac{c-1}{x}+d-d=cd-d\\\\\frac{c-1}{x}=cd-d[/tex]
Multiply both sides of the equation by "x":
[tex](\frac{c-1}{x})x=x(cd-d)\\\\c-1=x(cd-d)[/tex]
Divide both sides of the equation by [tex](cd-d)[/tex]:
[tex]\frac{c-1}{cd-d}=\frac{x(cd-d)}{cd-d}\\\\\frac{c-1}{cd-d}=x[/tex]
Factor out "d" in the denominator and simplify. Therefore:
[tex]\frac{(c-1)}{d(c-1)}=x\\\\x=\frac{1}{d}[/tex]
