Question

Rewrite as equivalent rational expressions with denominator (3x-8)(x-5)(x-3)

4/3x²=23x+40, 9x/3x²-17x+24
Provide your answer below:
__/(3x-8)(x-3), __/(3x-8)(x-5)(x-3)

Answer 1

To rewrite the rational expressions with the given denominator, multiply both sides by the denominator and simplify. The equivalent rational expressions are 4/(3x-8)(x-3) and 9x/(3x-8)(x-5)(x-3).

Step-by-step explanation:

To rewrite the rational expressions with the given denominator, we need to find the equivalent numerators. Let's start with the first expression:

4/3x² = 23x + 40

Multiply both sides by the denominator (3x-8)(x-5)(x-3):

(3x-8)(x-5)(x-3) * 4/3x² = (3x-8)(x-5)(x-3) * (23x + 40)

The denominator will cancel out on the left side, leaving us with:

4 = (3x-8)(x-5)(x-3) * (23x + 40)

Now, let's move on to the second expression:

9x / (3x² -17x + 24)

Multiply both sides by the denominator (3x-8)(x-5)(x-3):

(3x-8)(x-5)(x-3) * 9x / (3x² -17x + 24) = (3x-8)(x-5)(x-3)

This time, the denominator will cancel out on the right side, giving us:

9x = (3x-8)(x-5)(x-3)

Therefore, the equivalent rational expressions are:

4/(3x-8)(x-3) and 9x/(3x-8)(x-5)(x-3)