Questions: State the excluded value for the rational equation. [ frac42 x-1=frac53 x+2 ] Select one: A. (x=-frac23, frac12) B. (x=-frac12, frac23) C. (x=-frac23) D. (x=frac12)

Solution Steps

To find the excluded values for the rational equation, we need to determine the values of \( x \) that make the denominators zero. These values are excluded because division by zero is undefined.

1. Set each denominator equal to zero and solve for \( x \).
2. The solutions to these equations are the excluded values.

The rational equation given is

\[ \frac{4}{2x - 1} = \frac{5}{3x + 2} \]

The denominators are \( 2x - 1 \) and \( 3x + 2 \).

To find the excluded values, we set each denominator equal to zero:

1. For \( 2x - 1 = 0 \): \[ 2x = 1 \implies x = \frac{1}{2} \]

2. For \( 3x + 2 = 0 \): \[ 3x = -2 \implies x = -\frac{2}{3} \]

The excluded values from the denominators are \( x = \frac{1}{2} \) and \( x = -\frac{2}{3} \).

Final Answer