The first "punishment" in any advanced algebra PDF is simplification of complex fractions.
Example Problem: Simplify: $$\frac\fracxx+y - \fracxx-y\fracyx+y + \fracyx-y$$
Solution Strategy:
Verdict: Mary Rojas wants you to remember that the answer is simply -1, regardless of $x$ and $y$ (as long as valid).
The infamous "Mary Rojas" problem often involves a system that looks impossible without a trick. me las vas a pagar mary rojas pdf %C3%A1lgebra
Example: $$x^2 + y^2 = 25$$ $$x^2 - y^2 = 7$$
Solution: Add them: $2x^2 = 32 \rightarrow x^2 = 16 \rightarrow x = \pm 4$. Subtract them (second from first): $(x^2+y^2) - (x^2-y^2) = 25-7 \rightarrow 2y^2 = 18 \rightarrow y^2 = 9 \rightarrow y = \pm 3$. Solutions: $(4,3), (4,-3), (-4,3), (-4,-3)$. The first "punishment" in any advanced algebra PDF
Example: $$\sqrtx+5 + \sqrtx = 5$$
Solution: Isolate one root: $\sqrtx+5 = 5 - \sqrtx$. Square both sides: $x+5 = 25 - 10\sqrtx + x$. Simplify: $5 = 25 - 10\sqrtx \rightarrow -20 = -10\sqrtx \rightarrow \sqrtx = 2$. Thus $x = 4$. Verify: $\sqrt9 + \sqrt4 = 3+2=5$. Valid. Verdict: Mary Rojas wants you to remember that
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