Solve 5/2y=4/y+1/4

$$\frac { 5 } { 2 y } = \frac { 4 } { y } + \frac { 1 } { 4 }$$

Solve for y

$$y=-6$$

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 4y, the least common multiple of 2y,y,4.

$$2\times 5=4\times 4+4y\times \frac{1}{4}$$

Multiply 2 and 5 to get 10.

$$10=4\times 4+4y\times \frac{1}{4}$$

Multiply 4 and 4 to get 16.

$$10=16+4y\times \frac{1}{4}$$

Multiply 4 and \frac{1}{4} to get 1.

$$10=16+y$$

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

$$16+y=10$$

Subtract 16 from both sides.

$$y=10-16$$

Subtract 16 from 10 to get -6.

$$y=-6$$