Question

Add and subtract and simplify the result. Specify the values that must be excluded from the domain.

Answer 1

The simplified polynomial expression is given as follows:

(2x² + x + 6)/[(x + 5)(x - 8)]

The values x = -5 and x = 8 are excluded from the domain.

How to find the simplified polynomial expression?

When polynomial expressions involve addition or subtraction, we combine the like terms, for multiplication, we apply the distributive property, multiplying all terms, and for division, we apply the last common multiple.

For this problem, the expression is given by:

$\frac{5x^2 - 25x - 4}{x^2 - 3x - 40} + \frac{2}{x - 8} - \frac{3x}{x + 5}$

The factors are given as follows:

x² - 3x - 40, x - 8, x + 5.

The multiplication of the last two is given by:

(x - 8)(x + 5) = x² - 3x - 40.

Hence (x - 8)(x + 5) is the least common factor, and the equivalent expression is found as follows:

$\frac{5x^2 - 25x - 4}{x^2 - 3x - 40} + \frac{2}{x - 8} - \frac{3x}{x + 5} = \frac{5x^2 - 25x - 4 + 2(x + 5) - 3x(x - 8)}{(x - 8)(x + 5)}$

The numerator is simplified as follows:

5x² - 25x - 4 + 2(x + 5) - 3x(x - 8) = 5x² - 25x - 4 + 2x + 10 - 3x² + 24x = 2x² + x + 6.

The denominator is the lcm, hence the simplified expression is:

(2x² + x + 6)/[(x + 5)(x - 8)]

The values x = -5 and x = 8 are excluded from the domain, as a fraction cannot have a denominator of 0.

More can be learned about polynomial expressions at brainly.com/question/2833285

#SPJ1