[tex] \\
\
x^2+\frac{3x}{x^2}-2x+1\\
\\
\text{Here the LCD is }x^2\\
\\
=\frac{x^2*x^2+3x-2x*x^2+x^2}{x^2}\\
\\
\text{Now Simplify we get}\\
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=\frac{x^4+3x-2x^3+x^2}{x^2}\\
\\
=\frac{x(x^3+3-2x^2+x)}{x*x}\\
\\
\text{Simplify we get}\\
\\
=\frac{x^3-2x^2+x+3}{x}\\ [/tex]
The given expression can be written as :
[tex] \frac{x^{2}+3x}{x^{2}-2x+1} =\frac{x(x+3)}{(x-1)(x-1)} [/tex]
In the numerator x can be taken as a common factor to give x(x+3x)
In denominator the first factors are x in both the parenthesis .We then find two numbers which when multiplied will give us 1 and the same numbers on addition should give us -2.The numbers are -1 and -1 .These are written next to x in both the parenthesis .The factors of denominator are (x-1)(x-1) .This can not be simplified further.
