Rearrange the equation by adding -8 to both sides to get:
\[\simplify{{t} / ({a} * x + {b}) = {d} + { -c} = {d -c}}\]
This gives \[\simplify{({a} * x + {b}) / {t} = 1 / {d -c}}\] (this is because if $\displaystyle \frac{a}{b}=c$ then $\displaystyle \frac{b}{a}=\frac{1}{c}$ on turning the fraction round the other way)
and so \[\simplify{({a} * x + {b}) = {t} / {d -c}}\] on multiplying both sides by 2.
Hence \[\simplify{{a} * x = {t} / {d -c} -{b} = ({a * an1} / {an2})}\]
and so \[\simplify{x={an1}/{an2}}\] is the solution on dividing both sides by 6.

Given the equation \[\simplify[std]{{a} * x + {b} = {f}/{g}({c} * x + {d})}\] we first multiply both sides by $\var{g}$ to get

\[\simplify[std]{{g}*({a} * x + {b} )= {f}*({c} * x + {d})}.\]

Then expand both sides of this equation to get:

\[\simplify[std]{{g*a} x + {g*b} = {f*c}x + {f*d}}.\]

and then collect together all the constant terms on the right hand-side, and collect together all the terms in $x$ on the left-hand side of the equation.

The equation can then be written as:
\[\simplify[std]{({g*a}-{f*c})x=({f*d}+{-g*b})}\] i.e.
\[\simplify{{g*a-f*c}x={f*d-b*g}}\]
which gives \[x =\simplify[std]{{(f*d-b*g)}/{(g*a-f*c)}}\] as the solution.

Check the answer

You can check that this is the correct solution by inputting this solution back into the equation to see if it satisfies the equation.