How do you solve for u in #4/(u+6)=6/(u+6)+2#?

Answer 1

#u=-7#

First, we need to put the requirements, that is #u!=-6# because then the denominator will be #0#, and make the equation undefined.

Then,

#4/(u+6)=6/(u+6)+2#
#-2/(u+6)=2#
#u+6=-1#
#u=-7#
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Answer 2

A different approach: #u=-7#

1 can take many different forms, but when you multiply by 1, the value remains unchanged.

#color(green)(4/(u+6)=6/(u+6)+2 color(white)("d")->color(white)("d")4/(u+6)=6/(u+6)+[2color(red)(xx1)])#
#color(green)( color(white)("ddddddddddddddddd")->color(white)("d")4/(u+6)=6/(u+6)+[2color(red)(xx(u+6)/(u+6))])#
#color(green)(color(white)("dDDDDddddddddddd")->color(white)("d")4/(u+6)=6/(u+6)+color(white)("d")(2(u+6))/(u+6)#

We can now disregard the denominators, or bottom numbers, as they are all the same.

Or, as a purist would say: multiply all of both sides by #(u+6)#. This cancels out the denominators which is THE SAME THING!
#color(green)(4=6+2(u+6))#
#color(green)(4=6+2u+12)#
#color(green)(4=18+2u)#

Take 18 off of both sides.

#color(green)(2u=-14)#

Split each side in half.

#color(green)(u=-7)#
#color(blue)("Foot note: as "u" can only take on one value for this to work ")##color(blue)("and this is not -6 then we do not need to state that "x!=-6)#
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Answer 3

To solve for u in the equation 4/(u+6)=6/(u+6)+2, we can start by simplifying the equation. By subtracting 2 from both sides, we get 4/(u+6) - 2 = 6/(u+6). Simplifying further, we have 4/(u+6) - 2(u+6)/(u+6) = 6/(u+6). Combining like terms, we get (4 - 2(u+6))/(u+6) = 6/(u+6). Simplifying the numerator, we have (4 - 2u - 12)/(u+6) = 6/(u+6). Simplifying further, we get (-2u - 8)/(u+6) = 6/(u+6). To eliminate the denominators, we can cross-multiply, giving us (-2u - 8)(u+6) = 6(u+6). Expanding both sides, we have -2u^2 - 12u - 8u - 48 = 6u + 36. Combining like terms, we get -2u^2 - 20u - 48 = 6u + 36. Rearranging the equation, we have -2u^2 - 26u - 84 = 0. To solve this quadratic equation, we can factor or use the quadratic formula. Factoring, we have (u + 2)(2u + 21) = 0. Setting each factor equal to zero, we get u + 2 = 0 or 2u + 21 = 0. Solving these equations, we find u = -2 or u = -21/2. Therefore, the solutions for u in the given equation are u = -2 or u = -21/2.

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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.

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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