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How do you solve # ((x+1)/(2(x-1)))=((4x)/3)+(1/(x-1))#?

Answer 1

Isaiah Anthony

#x=3/4#

#(x+1)/(2(x-1))=(4x)/3+1/(x-1)#

#(x+1)/(2(x-1))-1/(x-1)=(4x)/3#

#(x+1-2)/(x-1)=(4x)/3#

#(x-1)/(x-1)=(4x)/3#

#1=(4x)/3#

#4x=3#

#x=3/4#

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Answer 2

Eva Adamson

To solve the equation ((x+1)/(2(x-1)))=((4x)/3)+(1/(x-1)), we can start by simplifying both sides of the equation. First, we can multiply both sides by 2(x-1) to eliminate the denominators. This gives us (x+1) = (8x/3) + (2/3).

Next, we can simplify further by multiplying both sides by 3 to eliminate the fraction on the right side. This gives us 3(x+1) = 8x + 2.

Expanding the left side, we get 3x + 3 = 8x + 2.

To isolate the x terms on one side, we can subtract 3x from both sides, which gives us 3 = 5x + 2.

Subtracting 2 from both sides, we have 1 = 5x.

Finally, dividing both sides by 5, we find that x = 1/5.

Therefore, the solution to the equation is x = 1/5.

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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.