Question

Given the equation: $\frac{(a-c)}{(x-a)}=m$, solve for $x$.

Answer 1

Solving for $x$:

$\frac{(a-c)}{(x-a)}=m$

Multiplying both sides of the equation by $(x-a)$:

$\begin{array}{rcl}& \Rightarrow & \frac{(a-c)(x-a)}{(x-a)}=m(x-a)\\ \Rightarrow (a-c)& =& m(x-a)\\ & \Rightarrow & a-c=mx-ma\\ & \Rightarrow & mx=a-c+ma\\ & \Rightarrow & x=\frac{a-c+ma}{m}\\ & \Rightarrow & x=\frac{a}{m}-\frac{c}{m}+a\end{array}$

Hence, the value of $x$ is $\frac{a}{m}-\frac{c}{m}+a$.