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How do you simplify #2/x + 3/(2x^3)#?

Answer 1

Hazel Anglin

=#(4x^2 +3)/(2x^3)#

Treat algebraic fractions the same as arithmetic fractions.

Find the LCD first and make equivalent fractions.

#2/x + 3/(2x^3) " "LCD = 2x^3#

#2/x xx (2x^2)/(2x^2) + 3/(2x^3)#

=#(4x^2 +3)/(2x^3)#

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Answer 2

Nathan Axel

To simplify the expression 2/x + 3/(2x^3), we need to find a common denominator and combine the fractions. The common denominator is 2x^3.

To convert the first fraction, we multiply the numerator and denominator by 2x^2 to get 4x^2/2x^3.

To convert the second fraction, we multiply the numerator and denominator by x^2 to get 3x^2/(2x^3).

Now, we can combine the fractions by adding the numerators and keeping the common denominator: (4x^2 + 3x^2)/(2x^3).

Simplifying the numerator gives us 7x^2, so the final simplified expression is 7x^2/(2x^3).

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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.