This is how every lesson in Math GRE Studio works: understand the idea, watch it applied, then try one yourself. Scroll down to start.
When you see a fraction like $\dfrac{x^2 - 9}{x^2 - 3x}$, it's tempting to "cancel" the $x^2$ from the top and bottom. But that's illegal — you can only cancel factors, not individual terms inside a sum.
The first step is always the same: factor the numerator and denominator completely, then see what's actually shared.
Rewrite the numerator and denominator as products:
$x^2 - 9$ is a difference of squares. $x^2 - 3x$ has a common factor of $x$.
Before you cancel anything, look at the original denominator $x(x-3)$ and find where it equals zero:
These restrictions survive simplification. Write them down now so you don't forget.
The factor $(x-3)$ appears in both numerator and denominator — cancel it:
Use the same three moves: factor, find restrictions, then cancel.
Concept first, worked example second, practice third. Every topic in Math GRE Studio follows this pattern — from algebra through analysis, in the right prerequisite order. This sample took about 3 minutes. Imagine a full study session where every topic builds on the last.
