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How do you solve #1/(x-6) + 1/(x-2)= 6/5 #?

Answer 1

Savannah Anderson

Solution : # x =7 ,x= 8/3 #

# 1/(x-6) +1/(x-2) = 6/5#. Multiplying by #5(x-6)(x-2)# on both

sides we get #5(x-2)+5(x-6)=6(x-6)(x-2) # or

#5x-10+5x-30=6(x^2-8x+12) #or

#10x-40= 6x^2-48x+72# or

#6x^2-48x+72-10x+40=0 or 6x^2-58x+112 =0 # or

#3x^2-29x+56 =0 or 3x^2-21x -8x+56 =0# or

# 3x(x-7)-8(x-7) =0 or (x-7)(3x-8) =0#

# :. x =7 ,x= 8/3 :.# Solution : # x =7 ,x= 8/3 # [Ans]

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Answer 2

Julia Adams

To solve the equation 1/(x-6) + 1/(x-2) = 6/5, we can start by finding a common denominator for the fractions on the left side. The common denominator is (x-6)(x-2). Multiplying each term by this common denominator, we get (x-2) + (x-6) = (6/5)(x-6)(x-2). Simplifying the equation, we have 2x - 8 = (6/5)(x^2 - 8x + 12). Expanding and rearranging, we obtain 2x - 8 = (6/5)x^2 - (48/5)x + (72/5). Moving all terms to one side, we have (6/5)x^2 - (58/5)x + (152/5) = 0. This is a quadratic equation. We can solve it by factoring, completing the square, or using the quadratic formula.

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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.