Art of Problem Solving: Introduction to Multi-Variable Equations

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Art of Problem Solving's Richard Rusczyk solves some multi-variable equations for one variable in terms of the other variables in the equations.
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At 9:00 instead of factoring out the r... why couldn't we just divide the 2rs-3r by itself, 2rs-3r? And then divide the other side by 2rs-3r?

horizonbrave
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R's on both sides!! NOOO!! :P Great video...love your channel AoPS

horizonbrave
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why does this only have 300 views? it should have a lot more!

jaydenshi
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also, r is supposed to equal stuff that IS r or it doesn't make sense that r doesn't equal r.

quincycostello
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Why so much plus, minus, multiplication and division business. Just follow the Rule- side change, sign change. To solve equations will be neat and clean, not cumbrous with vertical dangling of addition, subtraction, multiplication and division operations.

biswanathbera