How do you multiply #(2x) / (x+2) - 2 = (x-8) / (x-2)#?

Answer 1

#x=-4 or x=6#

#(2x)/(x+2)-2=(x-8)/(x-2)#
#:.=(2x(x-2)-2(x+2)(x-2)=(x+2)(x-8))/((x+2)(x-2))#
Multiply both sides by #(x+2)(x-2)#
#:.=2x(x-2)-2(x+2)(x-2)=(x+2)(x-8)#
#:.=2x^2-4x-2x^2+8=x^2-6x-16#
#:.=2x^2-x^2-2x^2-4x+6x+8+16=0#
#:.=-x^2+2x+24=0#
multiply both sides by#-1#
#:.=x^2-2x-24=0#
#:.=(x+4)(x-6)=0#
#:.=x=-4 or x=6#
check:-
substitute #x=-4#
#:.=(2(-4))/((-4)+2)-2=((-4)-8)/((-4)-2)#
#:.=(-8)/-2-2=(-12)/-6#
#:.=4-2=2#
substitute #x=6#
#(2(6))/((6)+2)-2=((6)-8)/((6-2))#
#:.=12/8-2=(-2)/4#
#:.=3/2-2=-1/2#
#1 1/2-2=-1/2#
#:.=-1/2=-1/2#
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Answer 2

To solve the equation (2x) / (x+2) - 2 = (x-8) / (x-2), we can follow these steps:

  1. Start by multiplying both sides of the equation by (x+2)(x-2) to eliminate the denominators.

  2. Simplify the equation by distributing and combining like terms.

  3. Rearrange the equation to isolate the variable x.

  4. Solve for x by applying the appropriate algebraic operations.

The detailed solution is as follows:

Step 1: Multiply both sides by (x+2)(x-2): (x+2)(x-2) * [(2x) / (x+2) - 2] = (x+2)(x-2) * [(x-8) / (x-2)]

Step 2: Simplify the equation: 2x(x-2) - 2(x+2)(x-2) = (x-8)(x+2)

Step 3: Expand and simplify: 2x^2 - 4x - 2(x^2 - 4) = x^2 - 6x - 16

Step 4: Continue simplifying: 2x^2 - 4x - 2x^2 + 8 = x^2 - 6x - 16

Step 5: Combine like terms: -4x + 8 = -6x - 16

Step 6: Move all terms involving x to one side: -4x + 6x = -16 - 8

Step 7: Simplify: 2x = -24

Step 8: Solve for x by dividing both sides by 2: x = -12

Therefore, the solution to the equation (2x) / (x+2) - 2 = (x-8) / (x-2) is x = -12.

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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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