Question

What is the simplified form of the following expression?

[(5x² 2x-3)/(5x²-33x 18)]/[(x²-6x 8)/(3x²-2x-8)]
A. (5x + 3) / (x - 6)
B. (5x - 3) / (x + 6)
C. (5x² - 3) / (x² - 6x + 8)
D. (x² - 6x + 8) / (5x² - 33x + 18)
E. (5x² + 2x - 3) / (3x² - 2x - 8)

Answer 1

To simplify the given expression, we need to simplify each individual fraction and then divide them. The simplified form of the expression is (5x + 3) / (3x + 2).

Step-by-step explanation:

To simplify this expression, we need to simplify each individual fraction and then divide them. Let's simplify each fraction one by one:

First, simplify the numerator of the first fraction:

5x² + 2x - 3 can't be factored further, so it remains the same.

Next, simplify the denominator of the first fraction:

5x² - 33x + 18 can be factored into (x - 3)(5x - 6).

Now, simplify the numerator of the second fraction:

x² - 6x + 8 can be factored into (x - 4)(x - 2).

Finally, simplify the denominator of the second fraction:

3x² - 2x - 8 can be factored into (x - 4)(3x + 2).

The simplified form of the expression is [(5x² + 2x - 3)/(x - 3)(5x - 6)] / [(x - 4)(x - 2)/(x - 4)(3x + 2)].

Simplifying further, we can cancel out like terms in the numerator and denominator:

The simplified form of the expression is (5x + 3) / (3x + 2).

So, the correct answer is A. (5x + 3) / (3x + 2).