Answer
$$\frac{VL + SN}{L + N} = C$$
Work Step by Step
$$V = C - \frac{C-S}{L}N$$ The easiest way to face this problem is to separate the fraction term. Taking into account that the variable $N$ is multiplied to the entire fraction, we use the Distributive property and re-write as follows: $$V = C - \frac{(CN - SN)}{L}$$ $$V = C - \frac{CN}{L} - \frac{SN}{L}$$ We can now isolate the terms including $C$: $$V + \frac{SN}{L} = C - \frac{CN}{L}$$ The next step is to apply the Distributive Property yet again to re-write the equation as follows: $$V + \frac{SN}{L} = C(1 - \frac{N}{L})$$ We can now divide both sides of the equation by the term beside $C$ to reach: $$\frac{V + \frac{SN}{L}}{1-\frac{N}{L}} = C$$ We can further simplify the equation by simplifying the fractions: $$\frac{\frac{VL}{L} + \frac{SN}{L}}{\frac{1L}{L} + \frac{N}{L}} = C$$
$$\frac{\frac{VL + SN}{L}}{\frac{L+N}{L}} = C$$ And since dividing fractions is the same as multiplying by the reciprocal: $$\frac{VL + SN}{L} \times \frac{L}{L + N} = C$$ Which simplifies into: $$\frac{VL + SN}{L + N} = C$$
