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Solve for [tex][tex]$x$[/tex][/tex]:
[tex]\[ \frac{3x}{x-5} = \frac{15}{x-5} \][/tex]


Sagot :

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].