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.