How do you solve #x/(x^2-8)=2/x#?

Answer 1

#x=+-4#

Move everything from the denominator to the numerator first; to do this, multiply each side's denominator by the LCM.

#x(x^2-8)* x/(x^2-8)= 2/x *x(x^2-8)#
the #(x^2-8)# on the left side cancels out and the #x# on the right side cancels out
#x(cancel(x^2-8))* x/(cancel(x^2-8))= 2/cancelx *cancelx(x^2-8)#

which gives us the following:

#x*x=2*(x^2-8)#
after this we now have # x^2=2(x^2-8)#
next we remove the parentheses by multiplying each term by 2 now we have #x^2=2x^2-16#
next we will move the 16 to the other side to avoid working with negative numbers #16+x^2=2x^2#
then we will combine like terms by subtracting #x^2# #16=2x^2-x^2# leaving us with #16=x^2#
then we will get rid of the #x^2# by taking the square root of both sides #+-sqrt16#=#sqrtx^2#
now we have our final answer of #x=+-4#
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Answer 2

To solve the equation x/(x^2-8) = 2/x, we can start by cross-multiplying to eliminate the fractions. This gives us x * x = 2 * (x^2-8). Simplifying further, we have x^2 = 2x^2 - 16. Rearranging the equation, we get x^2 - 2x^2 = -16. Combining like terms, we have -x^2 = -16. Dividing both sides by -1, we get x^2 = 16. Taking the square root of both sides, we have x = ±4. Therefore, the solutions to the equation are x = 4 and x = -4.

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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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