Solve for \( x \). \[ \frac{x}{x-5}-3=\frac{5}{x-5} \] If there is more than one solutional equation that sepmplifies to linear Like binomial... If there is no solution, click on "No solution".
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To solve the equation \[ \frac{x}{x-5}-3=\frac{5}{x-5}, \] first, we can combine the fractions on the left side. We rewrite \(-3\) as \(-\frac{3(x-5)}{x-5}\) to have a common denominator: \[ \frac{x - 3(x-5)}{x-5} = \frac{5}{x-5}. \] Next, simplify the numerator: \[ \frac{x - 3x + 15}{x-5} = \frac{5}{x-5}. \] This simplifies to: \[ \frac{-2x + 15}{x-5} = \frac{5}{x-5}. \] Since the denominators are the same, we set the numerators equal to each other: \[ -2x + 15 = 5. \] Now, solve for \(x\): \[ -2x = 5 - 15, \] \[ -2x = -10, \] \[ x = 5. \] However, this value causes the original expression \((x-5)\) to be zero, resulting in an undefined expression in the fractions. Therefore, there are no valid solutions. No solution.
