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How do you solve #3/(x-3)=x/(x-3)-3/2#?

Answer 1

x=3

Suggestion, take #x/(x-3)# and throw it to the left side as you can see they have a common denominator. This gives you: #3/(x-3) - x/(x-3)# = #-3/2# #(3-x)/(x-3) = -3/2#. Now, you cross-multiply the right and left sides. #2*(3-x) = -3*(x-3)# #6 - 2x = -3x + 9# (Just open the brackets) Now, rearrange terms: #-2x + 3x = 9-6# Which gives x = 3

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Answer 2

Hazel Anglin

To solve the equation 3/(x-3) = x/(x-3) - 3/2, we can start by multiplying both sides of the equation by (x-3) to eliminate the denominators. This gives us 3 = x - 3(x-3)/2. Simplifying further, we have 3 = x - (3x - 9)/2. Multiplying both sides by 2 to clear the fraction, we get 6 = 2x - (3x - 9). Combining like terms, we have 6 = 2x - 3x + 9. Simplifying, we get 6 = -x + 9. Subtracting 9 from both sides, we have -3 = -x. Multiplying both sides by -1, we get 3 = x. Therefore, the solution to the equation is x = 3.

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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.