Answer :
Using the least common denominator in simplifying the rational equation, the result in standard form is: x²-10x+8=0
The least common denominator is the smallest common multiple of the denominators of two or more fractions. It is useful when simplifying, adding, subtracting, or comparing fractions.
Given,
1/x + 1/ (x-2) = 1/4
The least common denominator of the two fractions on the left side of the equation is x(x - 2).
Thus,
[tex]\frac{1(x-2)+x(1)}{x(x-2)} =\frac{1}{4} \\\frac{x-2+x}{x(x-2)} =\frac{1}{4} \\\\\frac{2x-2}{2x - x^{2} } =\frac{1}{4} \\\\[/tex]
Cross multiplying:
4(2x+2)=1(x²-2x)
8x + 8 = x² -2x
Rewriting in standard form:
8x + 8 = x² -2x = x²-10x+8=0
To learn more about the least common denominator visit: brainly.com/question/542317
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