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How do you combine #3/(x+2)+(4/x)#?

Answer 1

Avery Alexander

Try by taking the common denominator #x(x+2)#: #(3x+4(x+2))/(x(x+2))=(3x+4x+8)/(x(x+2))=(7x+8)/(x(x+2))#

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Answer 2

Jameson Allen

To combine the expressions 3/(x+2) and 4/x, you need to find a common denominator. The common denominator for (x+2) and x is x(x+2).

To convert 3/(x+2) into an equivalent fraction with the common denominator, multiply the numerator and denominator by x: (3x)/(x(x+2)).

To convert 4/x into an equivalent fraction with the common denominator, multiply the numerator and denominator by (x+2): (4(x+2))/(x(x+2)).

Now, you can add the two fractions together: (3x)/(x(x+2)) + (4(x+2))/(x(x+2)).

Combine the numerators: (3x + 4(x+2))/(x(x+2)).

Simplify the numerator: (3x + 4x + 8)/(x(x+2)).

Combine like terms: (7x + 8)/(x(x+2)).

This is the simplified expression obtained by combining 3/(x+2) and 4/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.