# How do you simplify #(25c^3d^3e^3 - 55c^4d^5e^7 + 35c^8d^7e^6) / (5c^2d^2e^3)#?

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The simplified expression is 5c^3d^3e^3 - 11c^2d^3e^5 + 7c^6d^5e^3.

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To simplify ( \frac{25c^3d^3e^3 - 55c^4d^5e^7 + 35c^8d^7e^6}{5c^2d^2e^3} ), you divide each term in the numerator by the denominator. This yields:

[ \frac{25c^3d^3e^3}{5c^2d^2e^3} - \frac{55c^4d^5e^7}{5c^2d^2e^3} + \frac{35c^8d^7e^6}{5c^2d^2e^3} ]

Then, simplify each term individually:

[ \frac{25}{5} \cdot \frac{c^{3-2}}{c^{2-2}} \cdot \frac{d^{3-2}}{d^{2-2}} \cdot \frac{e^{3-3}}{e^{3-3}} - \frac{55}{5} \cdot \frac{c^{4-2}}{c^{2-2}} \cdot \frac{d^{5-2}}{d^{2-2}} \cdot \frac{e^{7-3}}{e^{3-3}} + \frac{35}{5} \cdot \frac{c^{8-2}}{c^{2-2}} \cdot \frac{d^{7-2}}{d^{2-2}} \cdot \frac{e^{6-3}}{e^{3-3}} ]

This simplifies to:

[ 5c \cdot d \cdot 1 - 11c^2 \cdot d^3 \cdot e^4 + 7c^6 \cdot d^5 \cdot e^3 ]

So, the simplified expression is ( 5cd - 11c^2d^3e^4 + 7c^6d^5e^3 ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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