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How do you simplify #\frac { 12x + 12} { 3- \frac { 3} { x^ { 2} } }#?

Answer 1

Genesis Allen

#=> x^2/ (x+1)#

#\frac { 12x + 12} { 3- \frac { 3} { x^ { 2} } }#

First we will calculate the denominator separately:

#{ 3- \frac { 3} { x^ { 2} } }#

#=> 3(x^2/x^2)- \frac { 3} { x^ { 2} } #

#=> (3x^2 - 3)/ x^2 #

Now we know #a-: b/c = axx c/b#

#therefore \frac { 12x + 12} { 3- \frac { 3} { x^ { 2} } }# can be written as:

# =>(12x + 12) xx ( frac { x^2} { 3x^ { 2} -3 } )#

# =>(cancel12^4(x + 1) xx x^2 ) /{ cancel3^1(x^ { 2} -1) } #

#=> (x^2(x+1))/ (x^2-1)#

Now substitute #(x^2-1) = (x+1)(x-1)#;

#=> (x^2(x+1))/( (x-1)(x+1))#

#=> (x^2cancel((x+1)))/( (x-1)cancel((x+1)))#

#=> x^2/ (x+1)#

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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.