Question

question
solve for all values of x:
\\(\frac{6}{x - 6}-1 = \frac{x}{x - 6}\\)

Explanation:

Step1: Multiply both sides by \(x - 6\) (note \(x

eq6\))
\(\frac{6}{x - 6}(x - 6)-1\times(x - 6)=\frac{x}{x - 6}(x - 6)\)
Simplify each term: \(6-(x - 6)=x\)

Step2: Simplify the left - hand side

Expand the left - hand side: \(6 - x+6=x\)
Combine like terms: \(12 - x=x\)

Step3: Solve for \(x\)

Add \(x\) to both sides: \(12=x + x\)
Which is \(12 = 2x\)
Divide both sides by 2: \(x=\frac{12}{2}=6\)

But we note that when \(x = 6\), the original equation has a denominator of \(x-6=0\), which makes the equation undefined. So there is no solution.

Answer:

No solution (since \(x = 6\) makes the original equation undefined)