2/w+ 4/w-1 = 10/w(w-1)

2(w-1)/w(w-1) + 4w/w(w-1)=10/w(w-1)
2w-2/w(w-1 +/4w/w(w-1= 10(w-1)/w(w-1)
2w-2+4w=10w-10
2w+4w-10w=-10-2
6w-10w=-10-2
-4w=8
w=2

w=2 satisfies the original equation, so I guess your solution is correct.

However, the steps should be

2(w-1)/2(w-1) + 4w/w(w-1) = 10/w(w-1)
2w-2 + 4w = 10
6w = 12
w = 2

To solve the equation 2/w + 4/(w-1) = 10/(w(w-1)), we need to find the value of w that satisfies the equation. Here's how:

Step 1: Simplify the left-hand side of the equation:

First, find the common denominator for the fractions on the left-hand side, which is w(w-1):

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

Next, simplify the fractions:

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

Step 2: Combine like terms:

(2w-2+4w)/(w(w-1)) = (6w-2)/(w(w-1))

Step 3: Set the equation equal to 10/(w(w-1)):

(6w-2)/(w(w-1)) = 10/(w(w-1))

Step 4: Cross-multiply:

(w(w-1))(6w-2) = (10/1)(w(w-1))

6w² - 2w = 10w(w-1)

Step 5: Expand and simplify:

6w² - 2w = 10w² - 10w

Step 6: Combine like terms and move all terms to one side:

6w² - 10w² - 2w + 10w = 0

-4w² + 8w = 0

Step 7: Factor out common terms if possible:

-4w(w - 2) = 0

Step 8: Set each factor equal to zero:

-4w = 0 or w - 2 = 0

Step 9: Solve for w:

For -4w = 0, divide both sides by -4 to find w:

w = 0

For w - 2 = 0, add 2 to both sides to find w:

w = 2

Therefore, the equation is satisfied for w = 0 and w = 2.