Answer:
[tex]\displaystyle y=\frac{3x}{x-1}[/tex]
Step-by-step explanation:
Solving Equations
We have the expression:
[tex]\displaystyle x=\frac{y}{y-3}[/tex]
And it's required to make y the subject.
It can be done by isolating y on the left side of the equation and the rest of the expression on the right side.
The first step is removing the denominator by multiplying both sides by y-3:
[tex]\displaystyle (y-3)x=(y-3)\frac{y}{y-3}[/tex]
Simplifying the right side:
[tex]\displaystyle (y-3)x=y[/tex]
Remove the parentheses:
[tex]yx-3x=y[/tex]
Move the y's to the left side and the rest of the expression to the right side:
[tex]yx-y=3x[/tex]
Factor out y:
[tex]y(x-1)=3x[/tex]
Divide by x-1:
[tex]\mathbf{\displaystyle y=\frac{3x}{x-1}}[/tex]
