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How do you solve # 2/(x-6)+6= x/(x-6)#?

Answer 1

Eli Assouline

# x=34/5#

#2/(x-6) + 6 = x/(x-6)#

#=> (2+6(x-6))/color(red)cancel(color(black)(x-6)) = x/color(red)cancel(color(black)(x-6))#

#=> 2+6x-36 = x#

#=> 6x-x-36+2=0#

#=> 5x=34#

#=> x=34/5#

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Answer 2

Nathan Axel

To solve the equation 2/(x-6) + 6 = x/(x-6), we can start by multiplying both sides of the equation by (x-6) to eliminate the denominators. This gives us 2 + 6(x-6) = x. Simplifying further, we have 2 + 6x - 36 = x. Combining like terms, we get 6x - x = 36 - 2, which simplifies to 5x = 34. Finally, dividing both sides by 5, we find x = 34/5.

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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.