Question

Need help on #3 Please help me on my hw

Answer 1

$\frac{6}{6+12x}\ne\frac{1}{1+12x}$

Factor the left hand side:

$\begin{gathered} \frac{6}{6}\cdot\frac{1}{1+2x}\ne\frac{1}{1+12x} \\ \frac{1}{1+2x}\ne\frac{1}{1+12x} \\ \end{gathered}$

$1+12x\ne1+2x$

Subtract 2x from both sides:

$\begin{gathered} 1+12x-2x\ne1+2x-2x \\ 1+10x\ne1 \end{gathered}$

Sutract 1 from both sides:

$\begin{gathered} 1+10x-1\ne1-1 \\ 10x\ne0 \end{gathered}$

Divide both sides by 10:

$\begin{gathered} \frac{10x}{10}\ne\frac{0}{10} \\ x\ne0 \end{gathered}$

Therefore, the equation is correct for every x different from 0.