Question

Solve the rational equation for x and state all x values that are excluded from the solution set. If there is more than one excluded value then separate them with a comma and do not include any spaces. \frac{3x}{x-1}+2=\frac{3}{x-1} Solving for x gives us x=AnswerThe value for x cannot equal Answer

Answer 1

It is already identified that
`\( x \)` cannot be equal to 1 due to the restriction from the denominators. This means there is no solution to the equation within the domain of real numbers.

The given rational equation is:

`\[ (3x)/(x-1) + 2 = (3)/(x-1) \]`

To find the value of
`\( x \)`, we need to solve this equation. However, before we do that, we should note the excluded values. These are the values of
`\( x \)` that would make any denominator zero, as division by zero is undefined.

From the equation, it's clear that
`\( x \)` cannot be equal to 1, as that would make the denominator of both rational expressions zero.

Now, let's solve the equation:

`\[ (3x)/(x-1) + (2(x-1))/(x-1) = (3)/(x-1) \]`

`\[ (3x)/(x-1) + (2x - 2)/(x-1) = (3)/(x-1) \]`

Combine the terms on the left-hand side:

`\[ (3x + 2x - 2)/(x-1) = (3)/(x-1) \]`

`\[ (5x - 2)/(x-1) = (3)/(x-1) \]`

Since the denominators are the same, the numerators must be equal for the two sides of the equation to be equal:

`\[ 5x - 2 = 3 \]`

`\[ 5x = 3 + 2 \]`

`\[ 5x = 5 \]`

`\[ x = (5)/(5) \]`

`\[ x = 1 \]`

However, we already identified that
`\( x \)` cannot be equal to 1 due to the restriction from the denominators. This means there is no solution to the equation within the domain of real numbers.

Answer 2

Step-by-step explanation:

Given the equation:

`(3x)/(x-1)+2=(3)/(x-1)`

Multiply the equation by x - 1

`\begin{gathered} 3x+2(x-1)=3 \\ 3x+2x-2=3 \\ 5x=3+2=5 \\ x=(5)/(5)=1 \end{gathered}`

But x cannot be equal to 1, as this would make the equation undefined.

The solution to this equation does not exist. You should consider excluded solutions first before s