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How do you solve for x in #1/x + 3/(x-1) = 7/2#?

Answer 1

Julia Adams

#x=1/7# or #x=2#

#1/x+3/(x-1)=7/2#

#((x-1)+3x)/(x(x-1))=7/2#

#(4x-1)/(x(x-1))=7/2#

#2(4x-1)=7x(x-1)#

#8x-2=7x^2-7x#

#7x^2-15x+2=0#

#(7x-1)(x-2)=0#

#x=1/7# or #x=2#

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Answer 2

Jameson Allen

To solve for x in the equation 1/x + 3/(x-1) = 7/2, we can start by finding a common denominator for the fractions. The common denominator is 2x(x-1). Multiplying each term by this common denominator, we get 2(x-1) + 6x = 7x(x-1). Simplifying the equation, we have 2x - 2 + 6x = 7x^2 - 7x. Combining like terms, we get 8x - 2 = 7x^2 - 7x. Rearranging the equation, we have 7x^2 - 15x + 2 = 0. This is a quadratic equation, which can be solved by factoring, completing the square, or using the quadratic formula. Solving for x, we find that x = 1/7 or x = 2/7.

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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.