How do you solve rational equations #81.9=((0.1+2x)^2)/((0.1x)(0.1x))#?
We can rewrite the dominator, to get
Expand the brackets
From the quadratic formula:
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To solve the rational equation 81.9 = ((0.1 + 2x)^2) / ((0.1  x)(0.1  x)), we can follow these steps:

Start by multiplying both sides of the equation by the denominators (0.1  x)(0.1  x) to eliminate the fractions.

Simplify the equation by expanding the numerator and multiplying the denominators.

Rearrange the equation to bring all terms to one side and set it equal to zero.

Combine like terms and simplify the equation further.

Solve the resulting quadratic equation by factoring, completing the square, or using the quadratic formula.

Check the solutions obtained by substituting them back into the original equation to ensure they are valid.
Please note that the solution to this specific equation may involve complex numbers.
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To solve the rational equation (81.9 = \frac{{(0.1 + 2x)^2}}{{(0.1  x)(0.1  x)}}):

Begin by multiplying both sides of the equation by the denominator ((0.1  x)(0.1  x)) to clear the fraction.

After multiplying, you should have an equation without any fractions.

Expand and simplify both sides of the equation using the distributive property and combining like terms.

Once you have simplified the equation, it should be a polynomial equation.

Solve the resulting polynomial equation for (x). This may involve factoring, using the quadratic formula, or other methods depending on the complexity of the equation.

Check any solutions you find by plugging them back into the original equation to ensure they are valid solutions.

If any solutions are extraneous (i.e., they make the denominator of the original rational equation equal to zero), discard them.

Any remaining solutions are the solutions to the rational equation.
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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