Question 6999
Well...I have never solved an equation with a cherry on top, but there's always a first time.

{{{(2x-3)/(4x-5) = 4/7}}} 

Cross-multiply;

{{{7(2x-3) = 4(4x-5)}}}

Simplify and solve for x.

{{{14x-21 = 16x-20}}}

Subtract 14x from both sides.

{{{-21 = 2x-20}}}

Add 20 to both sides.

{{{-1 = 2x}}}

Divide both sides by 2.

{{{x = -1/2}}}

Check:

{{{(2(-1/2)-3)/(4(-1/2)-5)}}} = {{{(-1-3)/(-2-5)}}} = {{{(-4)/-7}}} = {{{4/7}}}