What happens when a value causes a denominator in a fraction to be equal to zero?

When a value causes a denominator in a fraction to be equal to zero, **this fraction is undefined**. In mathematics, division by zero is not permitted, so any fraction that has a denominator of zero does not have a valid numerical value, and thus is considered undefined.

What happens when a value causes a denominator in a fraction to be equal to zero?

There are infinite solutions.
This fraction is undefined.
This value is a solution to the equation.
The value of the equation becomes zero.

When a value causes a denominator in a fraction to be equal to zero, **this fraction is undefined**. Division by zero is not allowed in mathematics, so any fraction with a denominator of zero does not have a meaningful or valid value. Therefore, the correct answer is "This fraction is undefined."

What value makes the equation -5 = 4 - 3x/4 - 3x undefined?

To determine the value that makes the equation

\[
-5 = \frac{4 - 3x}{4 - 3x}
\]

undefined, we need to look at the denominator of the fraction. The fraction becomes undefined when the denominator is equal to zero.

In this case, the expression \(4 - 3x\) appears in both the numerator and the denominator. For the fraction to be undefined, we set the denominator equal to zero:

\[
4 - 3x = 0
\]

Now, solve for \(x\):

1. Subtract 4 from both sides:

\[-3x = -4\]

2. Divide by -3:

\[x = \frac{-4}{-3} = \frac{4}{3}\]

Thus, the value \(x = \frac{4}{3}\) makes the fraction undefined.

Solve the equation for the variable k: 30/k +1 = 4

To solve the equation

\[
\frac{30}{k} + 1 = 4,
\]

follow these steps:

1. First, isolate the term with \(k\) by subtracting 1 from both sides:

\[
\frac{30}{k} = 4 - 1.
\]

This simplifies to:

\[
\frac{30}{k} = 3.
\]

2. Next, multiply both sides by \(k\) to eliminate the fraction:

\[
30 = 3k.
\]

3. Now, divide both sides by 3 to solve for \(k\):

\[
k = \frac{30}{3} = 10.
\]

Thus, the solution for \(k\) is

\[
\boxed{10}.
\]

What is the value for the variable f in 17/3f - 1 = 1

To solve the equation

\[
\frac{17}{3f} - 1 = 1,
\]

follow these steps:

1. **Add 1 to both sides** to isolate the fraction:

\[
\frac{17}{3f} = 1 + 1.
\]

This simplifies to:

\[
\frac{17}{3f} = 2.
\]

2. **Multiply both sides by \(3f\)** to eliminate the fraction:

\[
17 = 2 \cdot 3f.
\]

This simplifies to:

\[
17 = 6f.
\]

3. **Divide both sides by 6** to solve for \(f\):

\[
f = \frac{17}{6}.
\]

Thus, the value for the variable \(f\) is

\[
\boxed{\frac{17}{6}}.
\]

the options are

3
4
5
6

To find the value of \( f \) in the equation

\[
\frac{17}{3f} - 1 = 1,
\]

we can follow these steps carefully again, considering the answer options provided.

1. Rearrange the equation:

\[
\frac{17}{3f} = 1 + 1,
\]

which simplifies to:

\[
\frac{17}{3f} = 2.
\]

2. Multiply both sides by \( 3f \):

\[
17 = 2 \cdot 3f.
\]

3. This simplifies to:

\[
17 = 6f.
\]

4. Next, divide both sides by 6:

\[
f = \frac{17}{6}.
\]

Now let's approximate \(\frac{17}{6}\):

\[
\frac{17}{6} \approx 2.83.
\]

Among the provided options (3, 4, 5, 6), the closest integer value is **3**.

Thus, if you are asked to select the closest answer from the given options, the answer would be:

\[
\boxed{3}.
\]