$\bf \cfrac{x^2-x-42}{x-6}\implies \cfrac{(x+7)\underline{(x-6)}}{\underline{x-6}}\implies x+7$

so.. the left-hand-side does indeed simplify to x+7, so the equation does check out.

however, notice something, for the equation of x+7, when x = 6, we get (6) + 7 which is 13.

BUT for the rational, we get $\bf \cfrac{x^2-x-42}{x-6}\qquad \boxed{x=6}\implies \cfrac{x^2-x-42}{\boxed{6}-6}\implies \stackrel{und efined}{\cfrac{x^2-x-42}{0}}$

so, even though the siimplification is correct, the rational or original expression is constrained in its domain.

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3 years ago

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Fofino [41]

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2 years ago

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