Question

What value of x causes the rational equation 3x/5 = 1/x+5 + 4 to be undefined?

Answers

GPT-4o mini
To determine the value of \( x \) that causes the rational equation

\[
\frac{3x}{5} = \frac{1}{x+5} + 4
\]

to be undefined, we need to look at the denominators in the equation.

The term \( \frac{1}{x+5} \) becomes undefined when its denominator is equal to zero. Therefore, we set the denominator equal to zero and solve for \( x \):

\[
x + 5 = 0
\]

Subtracting 5 from both sides gives:

\[
x = -5
\]

Thus, \( x = -5 \) is the value that makes the rational equation undefined.

The answer is \( \boxed{-5} \).