Question

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

Answer 1

`\displaystyle y=(3x)/(x-1)`

Explanation:

Solving Equations

We have the expression:

`\displaystyle x=(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)(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=(3x)/(x-1)}`