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How do you simplify #\frac { 4y } { y ^ { 2} - 9} - \frac { 12} { y ^ { 2} - 9}#?

Answer 1

Avery Alexander

#=> 4/(y+3 )#

The denominator is the same...

#=> (4y-12)/(y^2-9) #

Factor #4y-12 -> 4(y-3) #

Use difference in two squares : #a^2 - b^2 = (a+b)(a-b) #

#=> y^2 - 9 -> (y+3)(y-3) #

#=> ( 4(y-3) ) / ( (y+3)(y-3) ) #

Cancel:

#=> ( 4cancel((y-3)) ) / ( (y+3)cancel((y-3)) ) #

#=> 4/(y+3 )#

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Answer 2

Abigail Allen

To simplify the expression \frac { 4y } { y ^ { 2} - 9} - \frac { 12} { y ^ { 2} - 9}, we can combine the two fractions by finding a common denominator. The denominators in both fractions are the same, y^2 - 9. Therefore, we can subtract the numerators directly and keep the common denominator. Simplifying the numerator gives us 4y - 12. Thus, the simplified expression is \frac { 4y - 12} { y ^ { 2} - 9}.

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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.