Alright, let's solve the equation step-by-step:
The given equation is:
[tex]\[
\frac{x-5}{x-1} \times 100 = 0
\][/tex]
1. Isolate the fraction:
To solve for [tex]\( x \)[/tex], we can first isolate the fraction by dividing both sides of the equation by 100. Since multiplying or dividing by a non-zero constant does not affect the equality, this simplifies to:
[tex]\[
\frac{x-5}{x-1} = 0
\][/tex]
2. Set the numerator equal to 0:
A fraction equals zero if and only if its numerator is zero (as long as the denominator is not zero). So, we need to set the numerator (which is [tex]\( x-5 \)[/tex]) to zero:
[tex]\[
x - 5 = 0
\][/tex]
3. Solve for [tex]\( x \)[/tex]:
Solve the equation [tex]\( x - 5 = 0 \)[/tex] by isolating [tex]\( x \)[/tex]:
[tex]\[
x = 5
\][/tex]
Therefore, the solution to the equation [tex]\(\frac{x-5}{x-1} \times 100 = 0\)[/tex] is:
[tex]\[
x = 5
\][/tex]
