How do you divide #\frac { - \frac { 5} { 28x ^ { 2} } } { \frac { 10} { 21x ^ { 3} } }#?

Answer 1

See the entire solution process below:

First, rewrite this expression using this rule for dividing fractions:

#(color(red)(a)/color(blue)(b))/(color(green)(c)/color(purple)(d)) = (color(red)(a) xx color(purple)(d))/(color(blue)(b) xx color(green)(c))#
#(color(red)(-5)/color(blue)(28x^2))/(color(green)(10)/color(purple)(21x^3)) = (color(red)(-5) xx color(purple)(21x^3))/(color(blue)(28x^2) xx color(green)(10))#

Next, cancel common terms with the constants in the numerator and denominator:

#(color(red)(-5) xx color(purple)(21x^3))/(color(blue)(28x^2) xx color(green)(10)) = (color(red)(-5) xx color(purple)((7 xx 3)x^3))/(color(blue)((7 xx 4)x^2) xx color(green)((5 xx 2))) = (-cancel(color(red)(5)) xx color(purple)((cancel(7) xx 3)x^3))/(color(blue)((cancel(7) xx 4)x^2) xx color(green)((cancel(5) xx 2))) =#
#-(3x^3)/(8x^2)#

Now, use these rules for exponents to complete the division:

#x^color(red)(a)/x^color(blue)(b) = x^(color(red)(a)-color(blue)(b))# and #a = a^color(red)(1)#
#-(3x^color(red)(3))/(8x^color(blue)(2)) = -(3x^(color(red)(3)-color(blue)(2)))/8 = -(3x^color(red)(1))/8 = -(3x)/8#
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Answer 2

To divide the expression (\frac{-\frac{5}{28x^2}}{\frac{10}{21x^3}}), you can multiply the numerator by the reciprocal of the denominator.

This means you can rewrite the expression as:

(\frac{-\frac{5}{28x^2}}{\frac{10}{21x^3}} = -\frac{5}{28x^2} \times \frac{21x^3}{10})

Next, you can simplify this expression:

(-\frac{5}{28x^2} \times \frac{21x^3}{10} = -\frac{5 \times 21x^3}{28x^2 \times 10})

Now, simplify the expression further:

(-\frac{5 \times 21x^3}{28x^2 \times 10} = -\frac{105x}{280})

So, the division of (\frac{-\frac{5}{28x^2}}{\frac{10}{21x^3}}) simplifies to (-\frac{105x}{280}).

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Answer from HIX Tutor

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.

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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