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 \( \boxed{-5} \).
\[
\frac{3x}{5} = \frac{1}{x+5} + 4
\]
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 \( \boxed{-5} \).