Question

solve the equation.\\(
\frac{x}{x - 7} = \frac{7}{x - 7} + 8\\)

Explanation:

Step1: Eliminate the denominator

Multiply both sides of the equation $\frac{x}{x - 7}=\frac{7}{x - 7}+8$ by $x - 7$ (note that $x
eq7$ to avoid division by zero). We get $x = 7+8(x - 7)$.

Step2: Expand and simplify

Expand the right - hand side: $x = 7+8x-56$. Then, move the terms with $x$ to one side and the constants to the other side. Subtract $8x$ from both sides: $x - 8x=7 - 56$. Combine like terms: $-7x=-49$.

Step3: Solve for x

Divide both sides by $-7$: $x=\frac{-49}{-7}=7$. But we need to check if this solution is valid. Since when $x = 7$, the original equation has a denominator of $x - 7=0$, this solution is extraneous. So, the equation has no solution.

Answer:

No solution