Questions: Rational Expressions Adding rational expressions with denominators ax-b and b-ax Subtract. 6/(8x-3) - 4/(3-8x) Simplify your answer as much as possible.

Solution Steps

To subtract these rational expressions, we first need to find a common denominator. Notice that the denominators \(8x - 3\) and \(3 - 8x\) are negatives of each other. Therefore, we can rewrite the second fraction to have the same denominator as the first by factoring out a negative sign. Once the denominators are the same, we can subtract the numerators and simplify the resulting expression.

We start with the rational expressions: \[ \frac{6}{8x - 3} - \frac{4}{3 - 8x} \]

Notice that \(3 - 8x\) can be rewritten as \(-(8x - 3)\). Thus, we can express the second fraction as: \[ \frac{4}{3 - 8x} = -\frac{4}{8x - 3} \]

Now, we can rewrite the subtraction with a common denominator: \[ \frac{6}{8x - 3} - \left(-\frac{4}{8x - 3}\right) = \frac{6 + 4}{8x - 3} = \frac{10}{8x - 3} \]

The resulting expression is already in its simplest form: \[ \frac{10}{8x - 3} \]

Final Answer