Question

X=(y)/(y-3) make y the subject

Answer 1

Answer:

$\displaystyle y=\frac{3x}{x-1}$

Step-by-step explanation:

Solving Equations

We have the expression:

$\displaystyle x=\frac{y}{y-3}$

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:

$\displaystyle (y-3)x=(y-3)\frac{y}{y-3}$

Simplifying the right side:

$\displaystyle (y-3)x=y$

Remove the parentheses:

$yx-3x=y$

Move the y's to the left side and the rest of the expression to the right side:

$yx-y=3x$

Factor out y:

$y(x-1)=3x$

Divide by x-1:

$\mathbf{\displaystyle y=\frac{3x}{x-1}}$