How do you simplify #(y^4/x^2)/((xy^2)/(2x^2))#?

Answer 1

#(2y^2)/x#

A complex fraction such as #(a/b)/(c/d)# can be written in a more familiar way:
#(a/b)/(c/d)# means the same as #(a/b) div (c/d)#

To divide by a fraction is the same as multiplying by its reciprocal.

#a/b color(limegreen)(div c/d) = a/b color(limegreen)(xx d/c) = (ad)/(bc)#

However if you compare this result to the original fraction you will see that we can simplify a complex fraction immediately:

#(color(red)(a)/color(blue)(b))/(color(blue)(c)/color(red)(d)) = color(red)(ad)/(color(blue)(bc))# Applying this to the complex fraction given gives us:
#(color(red)(y^4)/color(blue)(x^2))/(color(blue)(xy^2)/color(red)(2x^2)) = (color(red)(2x^2 xx y^4))/(color(blue)(x^2 xx xy^2))" "# which now simplifies to:
#=(2y^2)/x#
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Answer 2

#(2y^2)/x#

#(y^4/x^2)/((xy^2)/(2x^2))#
#:.y^4/x^2 xx (2x^2)/(xy^2#
#:.a^color(red)m*a^color(blue)n=a^(color(red)m+color(blue)n)#
#:.(y^color(red)(4-2) xx 2x^color(red)(2-2))/x^color(red)1#
#:.y^color(red)(4-2) xx 2x^color(red)(2-2-1)#
#:.y^color(red)2 xx 2x^color(red)(color(red)-1#
#:.y^color(red)2 xx 2 1/x^color(red)1#
#:.(2y^2)/x#
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Answer 3

To simplify the expression (y^4/x^2)/((xy^2)/(2x^2)), we can follow these steps:

  1. Invert the divisor and multiply: (y^4/x^2) * (2x^2/(xy^2))
  2. Simplify the numerator: y^4 * 2x^2 = 2x^2y^4
  3. Simplify the denominator: x^2 * xy^2 = x^3y^2
  4. Divide the numerator by the denominator: (2x^2y^4) / (x^3y^2)
  5. Simplify the expression by subtracting the exponents: 2x^(2-3)y^(4-2) = 2xy^2/x

Therefore, the simplified form of (y^4/x^2)/((xy^2)/(2x^2)) is 2xy^2/x.

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Answer 4

To simplify the expression (\frac{y^4/x^2}{\frac{xy^2}{2x^2}}), we follow these steps:

  1. Rewrite the expression as a division problem by multiplying by the reciprocal of the denominator: (\frac{y^4}{x^2} \times \frac{2x^2}{xy^2})

  2. Simplify each term in the expression: (\frac{y^4 \times 2x^2}{x^2 \times xy^2})

  3. Cancel out common factors between the numerator and denominator: (\frac{2y^4x^2}{x^3y^2})

  4. Reduce the expression by canceling out common factors: (\frac{2y^2}{x})

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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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