Question

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

Explanation:

Step1: Multiply both sides by \(x + 1\) (note \(x

eq - 1\))
\(6(x + 1)+x=-1\)

Step2: Expand the left - hand side

\(6x+6 + x=-1\)

Step3: Combine like terms

\(7x+6=-1\)

Step4: Subtract 6 from both sides

\(7x=-1 - 6\)
\(7x=-7\)

Step5: Divide both sides by 7

\(x=-1\)

But we need to check the domain. The original equation has a denominator of \(x + 1\), so \(x
eq - 1\). When we substitute \(x=-1\) back into the original equation, the denominators become zero, which makes the equation undefined. So there is no solution.

Answer:

No solution (or \(\text{No solution}\) since \(x = - 1\) makes the original equation undefined)