$$R=\frac{L}{L+D}$$

A streaming website uses the formula above to calculate the rating, $R$, of its films, based on the number of likes, $L$, and dislikes, $D$. Which of the following expresses the number of likes in terms of the other variables?

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Though this may seem difficult at first, it becomes trivial if we compare it to a similar case you've probably done before:

We can distribute the negative sign to the denominator to clean up the equation and match one of the options:

$$L=-\frac{RD}{R-1}$$ $$L =\frac{RD}{-(R-1)}$$ $$L=\frac{RD}{-R+1}$$ $$\boxed{L=\frac{RD}{1-R}}$$

You may be tempted to divide immediately, but we can only do so if we first take the reciprocal of both sides.

$$R=\frac{L}{L+D}$$ $$\frac{1}{R}=\frac{L+D}{L}$$ $$\frac{1}{R}=\frac{L}{L}+\frac{D}{L}$$ $$\frac{1}{R}=1+\frac{D}{L}$$ $$\frac{1}{R}-1=\frac{D}{L}$$ $$\frac{1}{R}-\frac{R}{R}=\frac{D}{L}$$ $$\frac{1-R}{R}=\frac{D}{L}$$ $$\frac{R}{1-R}=\frac{L}{D}$$ $$\boxed{L=\frac{RD}{1-R}}$$