X+4 over x^2-5x+6 ÷ x^2-16 over x+3

x =± 4

Step-by-step explanation:

Solve for x:

x^2 - 16 = 0

The left hand side factors into a product with two terms:

(x - 4) (x + 4) = 0

Split into two equations:

x - 4 = 0 or x + 4 = 0

Add 4 to both sides:

x = 4 or x + 4 = 0

Subtract 4 from both sides:

x =± 4

(x + 3) / (x - 2)(x - 3)(x - 4)

Step-by-step explanation:

The problem given can be viewed as

a/b over c/d

where a/b is the top fraction and c/d is the bottom fraction.

This can be rearranged to

a × d / b × c

So, you will have:

(x + 4)(x + 3) / (x² - 5x + 6)(x² - 16)

Now, factor the two bottom polynomials so you end up with:

(x + 4)(x + 3) / (x - 2)(x - 3)(x + 4)(x - 4)

Cancel the (x + 4) on the top and bottom so you’re left with the

(x + 3) / (x - 2)(x - 3)(x - 4)

If you need to find the solutions to x, set the denominator equal to zero.

x = 2

x = 3

x = 4