Solve 1/6y-1/5y=4/18-5/12

$$\frac{ 1 }{ 6y } - \frac{ 1 }{ 5y } = \frac{ 4 }{ 18 } - \frac{ 5 }{ 12 }$$

Solve for y

$$y=\frac{6}{35}\approx 0.171428571$$

Steps for Solving Linear Equation

Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 180y, the least common multiple of 6y,5y,18,12.

$$30-36=10y\times 4+180y\left(-\frac{5}{12}\right)$$

Subtract 36 from 30 to get -6.

$$-6=10y\times 4+180y\left(-\frac{5}{12}\right)$$

Multiply 10 and 4 to get 40.

$$-6=40y+180y\left(-\frac{5}{12}\right)$$

Multiply 180 and -\frac{5}{12} to get -75.

$$-6=40y-75y$$

Combine 40y and -75y to get -35y.

$$-6=-35y$$

Swap sides so that all variable terms are on the left hand side.

$$-35y=-6$$

Divide both sides by -35.

$$y=\frac{-6}{-35}$$

Fraction \frac{-6}{-35} can be simplified to \frac{6}{35} by removing the negative sign from both the numerator and the denominator.

$$y=\frac{6}{35}$$