How do you divide #x^2/(2x + 4)#?

Answer 1

There are several methods. I will try to show you long division.

Write the dividend with 0s for the missing terms:

#color(white)( (2x+4)/color(black)(2x+4))color(white)((x^2+0x+0))/(")" color(white)(x)x^2+0x + 0)#
Please observe that #x^2/(2x) = 1/2x#, therefore, we put #1/2x# in the quotient:
#color(white)( (2x+4)/color(black)(2x+4))(1/2xcolor(white)(0x+0))/(")" color(white)(x)x^2+0x + 0)#
We multiply #1/2x(2x+4) = x^2+2x# and then we subtract this underneath:
#color(white)( (2x+4)/color(black)(2x+4))(1/2xcolor(white)(0x+0))/(")" color(white)(x)x^2+0x + 0)# #color(white)(".............")ul(-x^2-2x)# #color(white)(".....................")-2x#
Please observe that #(-2x)/(2x) = -1#, therefore, we add #-1# in the quotient:
#color(white)( (2x+4)/color(black)(2x+4))(1/2x-1color(white)(+0))/(")" color(white)(x)x^2+0x + 0)# #color(white)(".............")ul(-x^2-2x)# #color(white)(".....................")-2x#
We multiply #-1(2x+4) = -2x-4# and then we subtract this underneath:
#color(white)( (2x+4)/color(black)(2x+4))(1/2x-1color(white)(+0))/(")" color(white)(x)x^2+0x + 0)# #color(white)(".............")ul(-x^2-2x)# #color(white)(".....................")-2x+0# #color(white)("........................")ul(2x+4)# #color(white)("................................")4" " larr# This is the remainder.
You can write the remainder as #4/(2x+4)# or #2/(x+2)#

The results of the division is:

#x^2/(2x + 4)= 1/2x-1+2/(x+2#
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Answer 2

To divide x^2 by (2x + 4), you can use polynomial long division. First, divide the highest degree term of the numerator (x^2) by the highest degree term of the denominator (2x). This gives you (1/2)x. Multiply this term by the entire denominator (2x + 4) and subtract the result from the numerator (x^2 - (1/2)x(2x + 4)). Simplify the resulting expression. Repeat this process until there are no more terms left in the numerator.

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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.

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.

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.

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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