Question 84530
Just set f(x) equal to zero. When you do that the given equation becomes:
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{{{3/(x-1) + 4/(x-2) = 0}}}
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Now get rid of the denominators by multiplying all terms (on both sides) of this equation 
by {{{(x-1)*(x-2)}}}. When you do that multiplication you get:
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{{{(3*(x-1)*(x-2))/(x-1) + (4*(x-1)*(x-2))/(x-2) = 0}}}
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Note that the right side of the equation remains zero because 0 times anything is still 
zero. Note also that you can now cancel the terms in the denominator with the same term 
in the numerator. The result is:
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{{{(3*(cross(x-1))*(x-2))/(cross(x-1)) + (4*(x-1)*(cross(x-2)))/(cross(x-2)) = 0}}}
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And the equation reduces to:
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{{{3*(x-2) + 4*(x-1) = 0}}}
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Multiply out the terms to get:
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3x - 6 + 4x - 4 = 0
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Combine the x terms and the equation becomes:
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7x – 6 – 4 = 0
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Combine the -6 with the -4 and the equation further becomes:
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7x – 10 = 0
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Eliminate the -10 from the left side by adding +10 to both sides. This makes the equation:
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7x = 10
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Finally, solve for x by dividing both sides of the equation by 7 which is the multiplier 
of the x term.  The division results in the answer:
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{{{x=10/7}}}
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Hope this helps you understand the problem.