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How do you simplify #(3x-2)/(6x) + (5x+1)/(9x)#?

Answer 1

Eli Assouline

#(x-4)/(18x)#

#(3x-2)/(6x)+(5x+1)//(9x)#

#color(white)("XXXX")#convert to a common denominator: #=(3x-2)/(6x)*3/3+(5x+1)/(9x)*2/2#

#=(9x-6)/(18x)+(10x+2)/(18x)#

#=(x-4)/(18x)#

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Answer 2

Kennedy Adams

To simplify the expression (3x-2)/(6x) + (5x+1)/(9x), we need to find a common denominator for the two fractions. The common denominator is 18x.

Next, we multiply the numerator and denominator of the first fraction (3x-2)/(6x) by 3 to get (9x-6)/(18x).

Similarly, we multiply the numerator and denominator of the second fraction (5x+1)/(9x) by 2 to get (10x+2)/(18x).

Now, we can combine the two fractions by adding their numerators and keeping the common denominator: (9x-6)/(18x) + (10x+2)/(18x).

Adding the numerators gives us (9x-6+10x+2)/(18x), which simplifies to (19x-4)/(18x).

Therefore, the simplified expression is (19x-4)/(18x).

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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.