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How do you simplify #\frac { 3x - 2} { 4- 6x } #?

Answer 1

Kennedy Adams

#-1/2#

Let's first notice that with the two #x# terms #3x# and #-6x#, we can say that:

#-2xx3x=-6x#

The same is true for the non-#x# terms:

#-2xx(-2)=4#

We are able to benefit from this:

#(3x-2)/(4-6x)#

#(3x-2)/((-2)(3x-2))#

We can now cancel out the #3x-2# terms and be left with:

#(cancel(3x-2))/((-2)(cancel(3x-2)))#

#1/(-2)=-1/2#

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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.

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