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How do you simplify #b/(b+3)+6/(b-2)#?

Answer 1

Ethan Adkins

#(b^2+4b +18)/((b+3)(b-2))#

Finding the LCD involves application of LCM;

LCM of #(b+3) and (b-2) = (b+3)(b-2)#

Multiply each fraction as necessary to create equivalent fractions.

#b/(b+3) xx(b-2)/(b-2)+6/(b-2) xx(b+3)/(b+3]#

Now simplify each fraction:

#(b(b-2))/((b+3)(b-2))+(6(b+3))/((b+3)(b-2))#

Now combine into one fraction:

#=(b^2-2b+6b+18)/((b+3)(b-2))#

#=(b^2+4b +18)/((b+3)(b-2))#

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Answer 2

Avery Alexander

To simplify the expression b/(b+3) + 6/(b-2), you need to find a common denominator for the two fractions. The common denominator is (b+3)(b-2).

Next, multiply the numerator and denominator of the first fraction b/(b+3) by (b-2), and multiply the numerator and denominator of the second fraction 6/(b-2) by (b+3).

This gives you (b(b-2))/((b+3)(b-2)) + (6(b+3))/((b+3)(b-2)).

Now, combine the numerators over the common denominator: (b(b-2) + 6(b+3))/((b+3)(b-2)).

Simplify the numerator: (b^2 - 2b + 6b + 18)/((b+3)(b-2)).

Combine like terms: (b^2 + 4b + 18)/((b+3)(b-2)).

Therefore, the simplified expression is (b^2 + 4b + 18)/((b+3)(b-2)).

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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.