Solve 8/4.5=y-2/frac{y{2}}

$$\frac{ 8 }{ 4.5 } = \frac{ y-2 }{ \frac{ y }{ 2 } }$$

Solve for y

$$y=18$$

Steps for Solving Linear Equation

Expand \frac{8}{4.5} by multiplying both numerator and the denominator by 10.

$$\frac{80}{45}=\frac{y-2}{\frac{y}{2}}$$

Reduce the fraction \frac{80}{45} to lowest terms by extracting and canceling out 5.

$$\frac{16}{9}=\frac{y-2}{\frac{y}{2}}$$

Divide y-2 by \frac{y}{2} by multiplying y-2 by the reciprocal of \frac{y}{2}.

$$\frac{16}{9}=\frac{\left(y-2\right)\times 2}{y}$$

Use the distributive property to multiply y-2 by 2.

$$\frac{16}{9}=\frac{2y-4}{y}$$

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

$$\frac{2y-4}{y}=\frac{16}{9}$$

Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 9y, the least common multiple of y,9.

$$9\left(2y-4\right)=16y$$

Use the distributive property to multiply 9 by 2y-4.

$$18y-36=16y$$

Subtract 16y from both sides.

$$18y-36-16y=0$$

Combine 18y and -16y to get 2y.

$$2y-36=0$$

Add 36 to both sides. Anything plus zero gives itself.

$$2y=36$$

Divide both sides by 2.

$$y=\frac{36}{2}$$

Divide 36 by 2 to get 18.

$$y=18$$