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How do you solve rational equations #7/(4x) - 3/x^2 = 1/(2x^2)#?

Answer 1

Eva Abramson

Place on an equivalent denominator.

The LCD (Least Common Denominator) is #4x^2#

7(x) - 3(4) = 1(2)

7x - 12 = 2

7x = 14

x = 2

Your solution is x = 2

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Answer 2

Hazel Anglin

To solve the rational equation 7/(4x) - 3/x^2 = 1/(2x^2), we can follow these steps:

Find a common denominator for all the fractions involved. In this case, the common denominator is 4x^2.
Multiply every term in the equation by the common denominator to eliminate the fractions.
Simplify the equation by distributing and combining like terms.
Rearrange the equation to have all the terms on one side and set it equal to zero.
Factor the resulting quadratic equation, if possible.
Solve for x by setting each factor equal to zero and solving for x.
Check the solutions obtained by substituting them back into the original equation to ensure they are valid.

By following these steps, you can solve the given rational equation.

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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.