Hello again! Can you people please help me in this math question?

(a) x/(x^2 + 6x + 8) = √576/(x + 2).


x/[(x + 2) * (x + 4)] = 24/(x + 2) <--- (*)Set: x + 2 ≠ 0 ---> x ≠ -2, and x + 4 ≠ 0 ---> x ≠ -4.


Multiply both sides by [(x + 2) * (x + 4)].

[(x + 2) * (x + 4)] * x/[(x + 2) * (x + 4)] = [(x + 2) * (x + 4)] * 24/(x + 2).


---> x = 24(x + 4).

x = 24x + 96.

x - 24x = 96.

-23x = 96.

x = -96/23 (Feasible solution, according to the solution set of the equation).

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

(b) 2x^2 + 7x + 6 = 0 <--- Use the quadratic formula in order to find the roots.


x = [-7 ± √(49 - 48)]/4 = (-7 ± 1)/4.


Either: x = (-7 - 1)/4 = -8/4 = -2 (Answer).

Or: x = (-7 + 1)/4 = -6/4 = -3/2 (Answer).


The only correct choice in your list is a) (Answer).

117.
x / (x² + 6x + 8) = √576 / (x + 2)
x / [(x + 2) (x + 4)] = 24 / (x + 2)

x + 2 ≠ 0 , then,
x / (x + 4) = 24
x = 24 (x + 4)
x = 24x + 96
-23x = 96
x = -96/23

The answer: d. -96/23


====
119.
2x² + 7x + 6 = 0
(2x + 3)(x + 2) = 0
2x + 3 = 0 or x + 2 = 0
x = -3/2 or x = -2

117)
x/(x^2 + 6x + 8) = √576/(x + 2)
x/(x^2 + 6x + 8) = 24/(x + 2)
24x^2 + 144x + 192 = x^2 + 2x
23x^2 + 142x + 192 = 0
(x + 2)(23x + 96) = 0
x = -2, -96/23 => reject x = -2 since it makes the denominator zero thus not in the domain
x = -96/23
d) => answer

118)
2x^2 + 7x + 6 = 0 => use the rational root theorem:

factors of 6 => ± (1, 2, 3, 6)
factors of 2 => ± (1, 2)
thus the possible rational roots are ± (1, 1/2, 2, 3/2, 3, 6) by inspection we find x = -2 is a root:
2(-2)^2 - 14 + 6 = 8 - 14 + 6 = 0 and we can find the other root by inspection or using synthetic division now let's verify by factoring:

2x^2 + 7x + 6 = 0
2x^2 + 4x + 3x + 6 = 0
2x(x + 2) + 3(x + 2) = 0
(x + 2)(2x + 3) = 0
x = -2, -3/2
a) => correct choice

x / (x² + 6x + 8) = √(576) / (x+2)

x / [(x+4)(x+2)] = 24 / (x+2)

x / (x+4) = 24

x = 24(x+4)
x = 24x + 96
23x = -96
x = -96/23

119.
2x² + 7x + 6 = 0
(2x+3)(x+2) = 0
x = -3/2 or -2