x = -1
Step-by-step explanation:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
          4/12-((x+2)/(2*x+5))=0
          x + 2
Simplify  ——————
          2x + 5    Â
              1
Simplify again  —
              3
1 Â Â Â (x + 2)
— - —————  = 0 Â
3 Â Â Â 2x + 5
Find the Least Common Multiple
   The left denominator is :    3 Â
   The right denominator is :    2x+5 Â
    Number of times each prime factor
    appears in the factorization of:
Prime Â
Factor  Left Â
Denominator  Right Â
Denominator  L.C.M = Max
{Left , Right} Â
3101
Product of all Â
Prime Factors  313
         Number of times each Algebraic Factor
      appears in the factorization of:
  Algebraic  Â
  Factor    Left Â
Denominator  Right Â
Denominator  L.C.M = Max Â
{Left , Right} Â
2x+5 Â 011
   Least Common Multiple:
   3 • (2x+5) Â
Denote the Least Common Multiple by  L.C.M Â
Denote the Left Multiplier by  Left_M Â
Denote the Right Multiplier by  Right_M Â
Denote the Left Deniminator by  L_Deno Â
Denote the Right Multiplier by  R_Deno Â
Left_M = L.C.M / L_Deno = 2x+5
Right_M = L.C.M / R_Deno = 3
Two fractions are called equivalent if they have the same numeric value.
Â
For example :  1/2  and  2/4  are equivalent,  y/(y+1)2  and  (y2+y)/(y+1)3  are equivalent as well.
To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.
 L. Mult. • L. Num.           2x+5  Â
 ——————————  =  ——————————
    L.C.M                3 • (2x+5)
 R. Mult. • R. Num.         (x+2) • 3
 ——————————  =  ——————————
    L.C.M               3 • (2x+5)
Add the two equivalent fractions which now have a common denominator
. Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
2x + 5 - ((x + 2) • 3)          -x - 1  Â
———————————  =  —————————
    3 • (2x + 5)           3 • (2x + 5)
Pull out like factors :
 -x - 1  =  -1 • (x + 1) Â
      -x - 1  Â
 —————————— = 0 Â
     3 • (2x + 5)
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now, to get rid of the denominator, multiply both sides of the equation by the denominator.
    -x - 1 Â
 ——————— • 3 • (2x + 5) = 0 • 3 • (2x + 5)
  3 • (2x + 5)
Now, on the left hand side, the  3 • 2x + 5  cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
 -x - 1  = 0
Solving a Single Variable Equation:
Solve  :   -x - 1 = 0 Â
Add  1  to both sides of the equation : Â
           -x = 1
Multiply both sides of the equation by (-1) : Â x = -1