4x/(x+6)(x+6) + 3/x-6=?

Question

Show how you got the answer

Answer 1

I think you mean 4x/((x+6)(x+6)) + 3/(x-6). You need a common denominator. In this case it will be (x+6)(x+6)(x-6).

So we get 4x(x-6) + 3(x+6)(x+6) as the new numerator.
This equals 4x^2-24x + 3x^2+36x+108 = 7x^2+12x+108.

Final answer: (7x^2+12x+108) / ((x+6)(x+6)(x-6))

Answer 2

Cross multiply

4x/(x+6)(x+6) + 3/x-6

4x (x-6) = 3 (x+6) (x+6)

4x² - 24 = 3x + 18 +3x + 18 (distributive property)

4x² = 6x + 60

4x² - 6x - 60 = 0

(2x - _ ) (2x + _ )

Find the missing numbers and solve for x, one answer might be negative, and one positive

Answer 3

Find the Least Common Denominator...

(x-6)(x+6)(x+6)

[(4x^2 - 24x) / (x-6)(x+6)(x+6)] + [3(x+6)^2 / (x-6)(x+6)(x+6)]

Add the numerators with the least common denominator remaining as the denominator.

[4x^2 - 24x + 3(x+6)^2] / [(x-6)(x+6)(x+6)]

Factor out the numerator.

1. 4x^2 - 24x = 4x(x-6)
2. 3(x+6)^2 = 3(x+6)(x+6)

Rewrite equation.

[4x(x-6) + 3(x+6)(x+6)] / [(x-6)(x+6)(x+6)]

All the parenthetical factors cancel out, and you are left with...

4x + 3

Answer 4

((4x)/((x + 6)(x + 6)) + (3/(x - 6))
Multiply everything by (x + 6)(x + 6)(x - 6)
(4x(x - 6) + 3((x + 6)(x + 6)))/((x + 6)(x + 6)(x - 6))
(4x^2 - 24x + 3(x^2 + 12x + 36))/((x + 6)(x + 6)(x - 6))
(4x^2 + 24x + 3x^2 + 36x + 108)/((x + 6)(x + 6)(x - 6))
(7x^2 + 60 + 108)/((x + 6)(x + 6)(x - 6))
((x + 6)(7x + 18))/((x + 6)(x + 6)(x - 6))

the (x + 6)s cancel out

(7x + 18)/((x + 6)(x - 6))

ANS : (7x + 18)/(x^2 - 36)

Answer 5

4x / ( (x+6) (x+6) ) + 3 / (x-6) =
( 4x (x-6) + 3 (x+6) (x+6) ) / (x+6)(x+6)(x-6) =
( 4x^2 - 24x + 3 (x^2 + 12x + 36) ) / (x+6)(x+6)(x-6) =
( 4x^2 - 24x + 3x^2 + 36x + 108) ) / (x+6)(x+6)(x-6) =
( 7x^2 + 12x + 108 ) / (x+6)(x+6)(x-6)

Answer 6

Assuming it is 3/(x-6)

4x/(x+6)^2 + 3/(x-6) = (4x(x-6)+3(x+6)^2)/(x+6)^2(x-6)

Now expand.

Answer 7

4x/(x+6)^2 +3/(x-6)= (7x^2 + 12 x +108)/((x-6)(x+6)^2)