Find the inverse of y = (5x-4) / (2x+3)

the aim of finsing the inverse is making x the subject. To start we need to multiply both sides by: (2x+3), giving us:

y(2x+3) = 5x-4

now we need to expand the brackets:

2xy +3y = 5x-4

now gather all the x components on the same side:

2xy - 5x = -4-3y

now factorise the left hand side:

x(2y-5) = -4-3y

now make x the subject, giving us:

x =(-4-3y) / (2y-5)

therefore, the inverse is written in terms of x, which gives us:

f^-1(x) = (-4-3y) / (2y-5)