3/(2m+4)= 1/(m+2)- 2
m=4
3/(2m+4) = 1/((m+2)-2)
STEP 1:
3*((m+2)-2) = 1*(2m+4)
STEP 2:
3m+6-6 = 2m+4
STEP 3:
3m = 2m+4 ----> 3m-2m = 4
FINAL
m = 4
To solve this equation, we will first multiply all terms by (2m + 4) in order to remove the denominators and simplify the equation.
Starting with:
3/(2m+4) = 1/(m+2) - 2
Multiply both sides by (2m + 4):
(2m + 4) * (3/(2m+4)) = (2m + 4) * (1/(m+2) - 2)
Simplifying the left side:
3 = (2m + 4) * (1/(m+2)) - (2m + 4) * 2
Next, distribute the terms on the right side:
3 = (2m + 4)/(m+2) - 2(2m + 4)
Now, simplify the right side of the equation:
3 = (2m + 4)/(m + 2) - (4m + 8)
To combine the fractions on the right side, we need a common denominator. Multiply the first fraction by (m + 2)/(m + 2) to get a common denominator:
3 = (2m + 4)/(m + 2) - (4m + 8) * (m + 2)/(m + 2)
Simplifying further:
3 = (2m + 4)/(m + 2) - (4m^2 + 8m + 8)/(m + 2)
Now, we can combine the fractions:
3 = (2m + 4 - (4m^2 + 8m + 8))/(m + 2)
Simplify the numerator:
3 = (2m + 4 - 4m^2 - 8m - 8)/(m + 2)
Rearrange the terms:
3 = (-4m^2 - 6m - 4)/(m + 2)
To make it easier to work with, let's multiply both sides by (m + 2) to eliminate the fraction:
3(m + 2) = -4m^2 - 6m - 4
Distribute 3 on the left side:
3m + 6 = -4m^2 - 6m - 4
Now, let's rearrange the equation to bring all terms to one side:
4m^2 + 9m + 10 = 0
At this point, the equation is in quadratic form. To solve it, we can use the quadratic formula:
m = (-b ± √(b^2 - 4ac))/(2a)
For our equation, a = 4, b = 9, and c = 10. Plugging these values into the quadratic formula, we can find the solution(s) for m.