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

Answer:

$x=\dfrac{1+r}{r}$

Step-by-step explanation:

Given equation:

$r=\dfrac{1}{(x-1)}$

Multiply both sides by (x - 1):

$\implies r(x-1)=\dfrac{1}{(x-1)} \cdot (x-1)$

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

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:

$\implies \dfrac{rx}{r}=\dfrac{1+r}{r}$

$\implies x=\dfrac{1+r}{r}$

Answer 2

Answer:

$x=\frac{1}{r} +1$

Step-by-step explanation:

$r=\frac{1}{x-1}$
$r(x-1)=1$
$x-1=\frac{1}{r}$
$x=\frac{1}{r} +1$