Questions: 8/(7x+7) = 5/(x+1) - 3/7 a. What is/are the value or values of the variable that make(s) the denominators zero? x=

Solution Steps

To find the values of the variable \( x \) that make the denominators zero, we need to set each denominator equal to zero and solve for \( x \). The denominators in the equation are \( 7x + 7 \) and \( x + 1 \). Solving these equations will give us the values of \( x \) that make the denominators zero.

The given equation is

\[ \frac{8}{7x+7} = \frac{5}{x+1} - \frac{3}{7} \]

The denominators in this equation are \(7x + 7\) and \(x + 1\).

To find the values of \(x\) that make the denominators zero, we set each denominator equal to zero and solve for \(x\).

1. For \(7x + 7 = 0\): \[ 7x + 7 = 0 \implies 7x = -7 \implies x = -1 \]

2. For \(x + 1 = 0\): \[ x + 1 = 0 \implies x = -1 \]

Both equations yield the same solution, \(x = -1\).

Final Answer