Math Question?

Question

Solve using the LCD (Lowest Common Denominator) and please explain work.
2/3x + 2/3 = 8/x+6

Answer 1

2/(3x) + (2/3) = 8/(x + 6)

The LCD of 3x, 3, and (x + 6) is 3x(x + 6), Multiplying both sides by 3x(x + 6) should eliminate all fractions.

2(x + 6) + (2)(x)(x + 6) = 8(3x)

2x + 12 + 2x^2 + 12x = 24x

Now, move everything to the left hand side, and put in descending power of x.

2x^2 + 14x - 24x + 12 = 0
2x^2 - 10x + 12 = 0

Divide both sides by 2,

x^2 - 5x + 6 = 0

Now, factor.

(x - 3)(x - 2) = 0

And solve.

x = {3, 2}

Answer 2

whoops** cannot divide both sides by 2 as there is a zero

good down to this point

2x^2 - 10x + 12 = 0
************************so
(2x-4)(x-3) = 0 should be our answer

x= 2
x = 3

Answer 3

IDK!!

Answer 4

idk??