Find the LCD for this expression: -11x^(2) / x^(2)+5x+6 = x^(2)+7x / x^(2)+7x+10. A (x−2)(x−3)? B (x+2)(x+3)(x+5). C (x+2)(x+3). D (x+6)? A B C OR D?

Answer 1

The answer is B

To find this, you need to factor the denominators on both sides of the equation

-11x²/(x²+5x+6) = -11x²/(x+2)(x+3)

(x²+7x)/(x²+7x+10) = (x²+7x)/(x+2)(x+5)

The question asks for the least common denominator. To find this, we need to be able to have the two denominators be the same value.

Multiply the denominator of the left side by the numerator and denominator on the right side:

(x²+7x)(x+2)(x+3)/(x+2)(x+5)(x+2)(x+3)

Next, multiply the denominator of the right side by the numerator and denominator on the right side:

(-11x²)(x+2)(x+5)/(x+2)(x+5)(x+2)(x+3)

Now, both sides of our equation have the same denominator. However, this is not the least common denominator, because we can simplify both sides. We see that we can cancel out (x+2) on both sides of the equation, which would leave us with these:

(x²+7x)(x+3)/(x+5)(x+2)(x+3)

(-11x²)(x+5)/(x+5)(x+2)(x+3)

Our denominators are still the same, but we cannot simplify any further. Therefore, the least common denominator is (x+2)(x+3)(x+5), which is choice B.

Answer 2

Given: (-11x^2 ) / (x^2 + 5x + 6) = (x^2 + 7x) / (x^2 + 7x + 10)

Find: LCD

Solution:

Factor everything and see what cancels.

(-11x^2 ) / (x^2 + 5x + 6) = (x^2 + 7x) / (x^2 + 7x + 10)

(-11x^2 ) / [(x+2)(x+3)] = [x(x+7)] / [(x+2)(x+5)]

Nothing cancels. Too bad.

The LCD will have factors from all denominators.

Do not include duplicates.

LCD = (x+2)(x+3)(x+5) The answer is B