# Solve the rational equation. \frac{x}{x-10}-6=\frac{10}{x-10}

Solve the rational equation.
$\frac{x}{x-10}-6=\frac{10}{x-10}$
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Arnold Odonnell

Step 1
Consider the equation $\frac{x}{x-10}-6=\frac{10}{x-10}$.
multiply both sides by (x-10) and simplify it
$\left(\frac{x}{x-10}\right)\left(x-10\right)-6\left(x-10\right)=\left(\frac{10}{x-10}\right)\left(x-10\right)$
$x-6\left(x-10\right)=10$
Step 2
use distributive property on $-6\left(x-10\right)$ and combine the like term
$x-6x+60=10$
$-5x+60=10$
subtract 60 both sides and simplify it
$-5x+60-60=10-60$
$-5x=-50$
Now divide both sides by -5 and simplify it
$\frac{-5x}{-5}=\frac{-50}{-5}$
$x=10$
Hence, the value of x=10.