Solve [3/2y/(frac{3y+y{2})}*100]=z

$$[ \frac { \frac { 3 } { 2 } y } { ( \frac { 3 y + y } { 2 } ) } \times 100 ] = z$$

Solve for y

$$y\neq 0$$

$$z=75\text{ and }y\neq 0$$

Steps for Solving Linear Equation

Divide \frac{3}{2}y by \frac{3y+y}{2} by multiplying \frac{3}{2}y by the reciprocal of \frac{3y+y}{2}.

$$\frac{\frac{3}{2}y\times 2}{3y+y}\times 100=z$$

Multiply \frac{3}{2} and 2 to get 3.

$$\frac{3y}{3y+y}\times 100=z$$

Combine 3y and y to get 4y.

$$\frac{3y}{4y}\times 100=z$$

Express \frac{3y}{4y}\times 100 as a single fraction.

$$\frac{3y\times 100}{4y}=z$$

Cancel out 4 in both numerator and denominator.

$$\frac{3\times 25y}{y}=z$$

Multiply 3 and 25 to get 75.

$$\frac{75y}{y}=z$$

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

$$75y=zy$$

Subtract zy from both sides.

$$75y-zy=0$$

Combine all terms containing y.

$$\left(75-z\right)y=0$$

Divide 0 by 75-z.

$$y=0$$

Variable y cannot be equal to 0.

$$y\in \emptyset$$

Solve for z

$$z=75$$

$$y\neq 0$$

Steps for Solving Linear Equation

Divide \frac{3}{2}y by \frac{3y+y}{2} by multiplying \frac{3}{2}y by the reciprocal of \frac{3y+y}{2}.

$$\frac{\frac{3}{2}y\times 2}{3y+y}\times 100=z$$

Multiply \frac{3}{2} and 2 to get 3.

$$\frac{3y}{3y+y}\times 100=z$$

Combine 3y and y to get 4y.

$$\frac{3y}{4y}\times 100=z$$

Cancel out y in both numerator and denominator.

$$\frac{3}{4}\times 100=z$$

Multiply \frac{3}{4} and 100 to get 75.

$$75=z$$

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

$$z=75$$