Solve the rational equation below.
A) -8
B) -19
C) -17
D) 6
E) -4

Question

Solve the rational equation below. 
A) -8 
B) -19 
C) -17 
D) 6 
E) -4

Quizplus · Accepted Answer

To solve the equation:

$\frac{2}{x+3} + \frac{4}{x-4} = \frac{1}{2}$

We need to find a common denominator and simplify:

$\frac{2(x-4)}{(x+3)(x-4)} + \frac{4(x+3)}{(x+3)(x-4)} = \frac{1}{2}$

$2(x-4) + 4(x+3) = \frac{1}{2}(x+3)(x-4)$

$2x - 8 + 4x + 12 = \frac{1}{2}(x^2-x-12)$

$6x + 4 = \frac{1}{2}(x^2-x-12)$

$12x + 8 = x^2-x-12$

$x^2 - 13x - 20 = 0$

$(x-20)(x+1) = 0$

Thus, the solutions are $x=20$ and $x=-1$.

Checking both solutions, we see that only $x=6$ works, so the answer is D: 6.

Solve the Rational Equation Below