Help! Any math wiz's out there?

Question

3x +1 3x + 5
______ - ______
x2-16 x2 + 8x+16??

I can't help my daughter with this math problem. Can any of you guys??

Answer 1

You have to find a common denominator

First, factor each denominator

x^2 - 16 = (x+4)(x-4)

x^2 + 8x + 16 = (x+4)(x+4) = (x+4)^2

The common denominator would be (x-4)(x+4)^2

The first term:

(3x+1)/{(x+4)(x-4)} is missing an (x+4) so multiply the top and bottom by x+4

{3x+1)(x+4)/{(x-4)(x+4)^2}

= (3x^2 + 13x +4)/{(x-4)(x+4)^2}

The second term

(3x+5)/(x+4)^2 is missing an x-4 so multiply the top and bottom by x-4

(3x+5)(x-4)/{(x-4)(x+4)^2}

= (3x^2 - 7x - 20)/{(x-4)(x+4)^2}

Now that there is a common denominator, you can just subtract the numerators

{3x^2 + 13x +4 - (3x^2 - 7x - 20)}/{(x-4)(x+4)^2}

= (3x^2 + 13x + 4 - 3x^2 + 7x + 20)/{(x-4)(x+4)^2}

Answer: (20x + 24)/{(x-4)(x+4)^2}

You can factor a 4 from the numerator but nothing will cancel with it, so this is an acceptable final answer.

Answer 2

(3x + 1)/(x² - 16) - (3x + 5)/(x² + 8x + 16)

given



(3x + 1)/(x + 4)(x - 4) - (3x + 5)/(x + 4)(x + 4)

factoring everything that can be factored



[(3x + 1)(x + 4) - (3x + 5)(x - 4)]/(x + 4)(x + 4)(x - 4)

since they are fractions, get LCD and combine them into 1 expression



(3x² + 13x + 4 - 3x² + 7x + 20)/(x + 4)(x + 4)(x - 4)

expanding



(20x + 24)/(x + 4)(x + 4)(x - 4)

combining like terms



4(5x + 6)/(x + 4)(x + 4)(x - 4)

factoring out



^_^

Answer 3

((3x + 1)/(x^2 - 16)) - ((3x + 5)/(x^2 + 8x + 16))

((3x + 1)/((x + 4)(x - 4))) - ((3x + 5)/((x + 4)(x + 4)))

Multiply everything by (x + 4)(x - 4)(x + 4)

(((3x+1)(x+4)) - ((3x+5)(x-4)))/((x+4)(x-4)(x+4))



((3x^2 + 12x + x + 4) - (3x^2 - 12x + 5x - 20))/((x + 4)(x + 4)(x - 4))



((3x^2 + 13x + 4) - (3x^2 - 7x - 20))/((x+4)(x+4)(x-4))

(3x^2 + 13x + 4 - 3x^2 + 7x + 20)/((x + 4)(x + 4)(x - 4))

(20x + 24)/((x + 4)(x + 4)(x - 4))

(4(5x + 6))/((x + 4)(x + 4)(x - 4))

since you can't simplify this any further

(20x + 24)/((x^2 - 16)(x + 4))

(20x + 24)/(x^3 + 4x^2 - 16x - 64)



ANS : (20x + 24)/(x^3 + 4x^2 - 16x - 64)

Answer 4

no im confused just looking at it

Answer 5

(20x+24)/((x+4)(x+4)(x-4))



or



(20x+24)/(x^3+4x^2-16x-64)

Answer 6

what does x = ?????