Get rid of fractions (by multiplying both sides by bvR)

$\begin{array}{rcl} b v R (\frac{m}{v} - \frac{t}{b}) & = & b v R \times \frac{(m - t)}{R} \\ \frac{b v R m}{v} - \frac{b v R t}{b} & = & \frac{b v R (m - t)}{R} \\ b R m - v R t & = & b v (m - t) \end{array}$

[1]

Expand the brackets on the right

$b R m - v R t = b v m - b v t$

Move all the m terms on to one side (for example, by subtracting bvm from both sides then adding vRt to both sides)

$\begin{array}{rcl} b R m - v R t - b v m & = & - b v t \\ b R m - b v m & = & v R t - b v t \end{array}$

[1]

Factorise m out of the terms on the left

$m (b R - b v) = v R t - b v t$

[1]

Get m on its own (by dividing both sides by bR - bv)

$m = \frac{v R t - b v t}{b R - b v}$ [1]

$m = \frac{b v t - v R t}{b v - b R}$ is also accepted

Rearranging Formula (Cambridge O Level Maths)

Exam Questions