Question

Solve the equation r = 1/(x-1) for x in terms of r. In other words, manipulate the equation until you have x equal to an expression with r's in it but no x's.

Answer 1

`x=(1)/(r) +1`

Explanation:

`r=(1)/(x-1)`

`r(x-1)=1`

`x-1=(1)/(r)`

`x=(1)/(r) +1`

Answer 2

`x=(1+r)/(r)`

Explanation:

Given equation:

`r=(1)/((x-1))`

Multiply both sides by (x - 1):

`\implies r(x-1)=(1)/((x-1)) \cdot (x-1)`

`\implies r(x-1)=1`

Expand the brackets:

`\implies rx-r=1`

Add r to both sides:

`\implies rx-r+r=1+r`

`\implies rx=1+r`

Divide both sides by r:

`\implies (rx)/(r)=(1+r)/(r)`

`\implies x=(1+r)/(r)`