5/6+1/5T=4/6

First, you need a common denominator -- the LCM of 5 and 6. What is that LCM?

30 Right.

5/6 = 25/30
1/5 = 6/30
4/6 = 20/30

25/30 + (6/30)t = 20/30
(6/30)t = (20/30) - (25/39
(6/30)t = -5/30
t = (-5/30) / (6/30)
t = (-5/30) * (30/6)
t = -150/180
t = -15/18 = -5/6

19/6+4y=8y-1/6

To solve the equation 5/6 + 1/5T = 4/6, we need to isolate the variable T on one side of the equation.

First, let's simplify the fractions by finding a common denominator. The least common multiple of 6 and 5 is 30, so we can rewrite the equation as:

(5/6)*(5/5) + (1/5T)*(6/6) = 4/6
25/30 + 6/30T = 4/6

Now, let's combine the fractions on the left-hand side of the equation:

(25 + 6/30T) = 4/6

To eliminate the fraction, we can multiply the entire equation by the 30T. This will give us:

30T * (25 + 6/30T) = (4/6) * 30T

On the left side, the 30T cancels out the denominator of 30T in the first term, leaving us with:

25 + 6 = (4/6) * 30T

Combine the like terms on the left side:

31 = (4/6) * 30T

To isolate T, divide both sides of the equation by (4/6) * 30:

31 / [(4/6) * 30] = T

Now, solve for T:

31 / [(4/6) * 30] = T

To simplify further, we can multiply the numerator and denominator by the reciprocal of (4/6), which is (6/4):

31 / [(4/6) * 30] = T
31 / [(4/6) * 30] * (6/4) = T

Simplify the expression:

31 * 6 / (4 * 30) = T

Now, calculate the result:

31 * 6 = 186
4 * 30 = 120

So, T = 186/120

The final result is T = 31/20, or if you prefer to write it as a decimal, approximately T = 1.55.