# How do you divide #(5x+15)/(12x-6) div(10x^2)/(18)#?

Your starting expression looks like this

Factor the numerator and the denominator of the first fraction to get

The expression will now become

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To divide (5x+15)/(12x-6) by (10x^2)/(18), you can simplify the expression by multiplying the numerator and denominator of the first fraction by the reciprocal of the second fraction.

First, find the reciprocal of (10x^2)/(18), which is (18)/(10x^2).

Next, multiply the numerator and denominator of (5x+15)/(12x-6) by (18)/(10x^2).

This results in (5x+15)/(12x-6) * (18)/(10x^2).

To simplify further, multiply the numerators and denominators together:

(5x+15)*(18) / (12x-6)*(10x^2).

Simplify the expression in the numerator:

90x + 270 / (12x-6)*(10x^2).

Simplify the expression in the denominator:

(12x-6)*(10x^2) = 120x^3 - 60x^2.

Therefore, the final simplified expression is:

(90x + 270) / (120x^3 - 60x^2).

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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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