Answer:
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
1
Simplify again —
3
1 (x + 2)
— - ————— = 0
3 2x + 5
Find the Least Common Multiple
The left denominator is : 3
The right denominator is : 2x+5
Number of times each prime factor
appears in the factorization of:
Prime
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left , Right}
3 1 0 1
Product of all
Prime Factors 3 1 3
Number of times each Algebraic Factor
appears in the factorization of:
Algebraic
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left , Right}
2x+5 0 1 1
Least Common Multiple:
3 • (2x+5)
Denote the Least Common Multiple by L.C.M
Denote the Left Multiplier by Left_M
Denote the Right Multiplier by Right_M
Denote the Left Deniminator by L_Deno
Denote the Right Multiplier by R_Deno
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.
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
—————————— = ——————————
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
——————————— = —————————
3 • (2x + 5) 3 • (2x + 5)
Pull out like factors :
-x - 1 = -1 • (x + 1)
-x - 1
—————————— = 0
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
——————— • 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
Add 1 to both sides of the equation :
-x = 1
Multiply both sides of the equation by (-1) : x = -1
