MHB Can You Simplify the Fraction 2h/h2 + 2h + 2 by Cancelling Out 2h?

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The fraction 2h/h² + 2h + 2 cannot be simplified by canceling out 2h. The expression simplifies to 2(1/h + h + 1), but 2h does not cancel out in this form. If the expression were 2h/(h² + 2h + 2), it still would not simplify further. Therefore, the initial assumption about canceling 2h is incorrect. The discussion clarifies the importance of correctly interpreting the fraction for simplification.
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2h/h2 + 2h + 2

does the 2h cancel out?
 
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coolbeans33 said:
2h/h2 + 2h + 2

does the 2h cancel out?

It's hard to see what you mean but I'm inclined to say the answer is no.

As you've written it we have:
$$\frac{2h}{h^2} + 2h + 2 = 2\left(\dfrac{1}{h} + h + 1\right)$$

but you can't cancel $$2h$$

If you meant $$\frac{2h}{h^2+2h+2}$$ then it won't cancel any further
 

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