Let's solve the equation [tex]\(\frac{3x}{x-5} = \frac{15}{x-5}\)[/tex] step by step.
1. Identify the given equation:
[tex]\[
\frac{3x}{x-5} = \frac{15}{x-5}
\][/tex]
2. Recognize that the denominators on both sides of the equation are identical. Since the denominators [tex]\(x-5\)[/tex] are the same and not equal to zero, we can set the numerators equal to each other:
[tex]\[
3x = 15
\][/tex]
3. Solve for [tex]\(x\)[/tex] by isolating [tex]\(x\)[/tex]. Divide both sides of the equation by 3:
[tex]\[
x = \frac{15}{3}
\][/tex]
4. Calculate the division on the right side:
[tex]\[
x = 5
\][/tex]
5. Conclude that the solution to the equation is:
[tex]\[
x = 5
\][/tex]
Therefore, the value of [tex]\(x\)[/tex] that satisfies the equation [tex]\(\frac{3x}{x-5} = \frac{15}{x-5}\)[/tex] is [tex]\(5\)[/tex].
