+0

# Solve for x

+1
78
1

Solve for x:

(3x + 12)/(x + 4) = (4x^2 + 5x + 8x^2)/(2x)

Apr 4, 2021

#1
+484
0

First, simplifying the right side gives $\frac{4x^2+5x+8x^2}{2x}=\frac{12x^2+5x}{2x}=\frac{12x+5}{2}$

Then, multiplying by $2(x+4)$ to get rid of fractions gives $2(3x+12)=(12x+5)(x+4)$.

Moving everything to one side gives $(12x+5)(x+4)-(6x+24)=0$.

Expanding everything gives $12x^2+53x+20-6x-24=0$.

Simplifying gives $12x^2+47x-4=0$.

Factoring this equation gives $(x-\frac{1}{12})(x+4)=0$.

So, our two solutions are $\frac{1}{12}$ and $-4$.

But wait!

$-4$ is extraneous, because plugging it in causes division by 0! That means $\boxed{x=\frac{1}{12}}$ is the only solution

Apr 4, 2021