1/m+2/m+1=4/m-1

Answer 1

To solve this equation, we need to find a common denominator for the fractions. The common denominator for m, 2/m, and 1 is m.

Therefore, we can rewrite the equation as:

1/m + 2/m + 1 = 4/m - 1
(1 + 2 + m)/m = (4 - m)/m

Now, we can combine like terms on both sides of the equation:

(3 + m)/m = (4 - m)/m
3 + m = 4 - m

Now, solve for m:

2m = 1
m = 1/2

Therefore, the solution to the equation is m = 1/2.

Answer 2

I expect the user meant
1/m + 2/(m+1) = 4/(m-1)
since your interpretation was rather trivial. If so, then
m = -3±2√2

Answer 3

Apologies for the misunderstanding. Let's solve the corrected equation:

1/m + 2/(m + 1) = 4/(m - 1)

To begin, we need to find a common denominator. The common denominator for the fractions on the left side is m(m + 1), and for the fraction on the right side, it is m - 1.

Multiplying each term by the respective denominator, we get:

(m + 1) + 2m = 4m(m + 1)/(m - 1)

Solving this equation step by step:

m + 1 + 2m = 4m(m + 1)/(m - 1)
3m + 1 = 4m(m + 1)/(m - 1)
3m + 1 = 4m^2 + 4m/(m - 1)

Rewriting the equation:

3m - 4m^2 - 4m = -1(1 - m)
4m^2 + 4m - 1 = 3m

Rearranging the equation:

4m^2 + m - 1 = 0

Now, we need to solve the quadratic equation for m. Using the quadratic formula:

m = [-1 ± sqrt(1^2 - 4*4*-1)] / 2*4
m = [-1 ± sqrt(1 + 16)] / 8
m = [-1 ± sqrt(17)] / 8

Therefore, the solutions for m are m = (-1 + sqrt(17))/8 and m = (-1 - sqrt(17))/8. Simplifying, we get m ≈ -0.195 and m ≈ -1.804.