write showing all working the following algebraic expression as a single fraction in its simplest form: 4-[(x+3)/ ((x^2 +5x +6)/(x-2))]

4-[(x+3)*((x-2)/(x^2 +5x +6))]

4-[(x+3)(x-2)/(x^2 +5x +6))]

factorise denominator 

4-[(x+3)(x-2)/(x+3)(x+2)]

cancel down (x+3)

4-[(x-2)/(x+2)]

expand 

4(x+2)/(x+2) - (x-2)/(x+2)

now share a denominator so make one fraction 

(4x+8-x+2)/(x+2)

simplify

(3x+10)/(x+2)