Simplify the complex fraction: ((3x-7)/x^2)/(x^2/2)+(2/x)

Simplify the complex fraction: ((3x-7)/x^2)/(x^2/2)+(2/x)

[tex] \dfrac{ \dfrac{3x-7}{x^2} }{ \dfrac{x^2}{2} } + \dfrac{2}{x} =\qquad \qquad x \neq 0\qquad x^4 \neq 0 \\ \\ \\ \dfrac{(3x-7)*2}{x^2*x^2}+ \dfrac{2}{x} = \\ \\ \\ \dfrac{6x-14}{x^4}+ \dfrac{2}{x} =\\ \\ \\ \dfrac{ 6x-14 }{ x^4 }+ \dfrac{2(x^3)}{x(x^3)}=\\ \\ \\ \boxed{ \dfrac{ 6x-14 +2x^3}{ x^4 } } [/tex]

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MrRoyal MrRoyal · Answer 2 · 2022-03-18T13:27:37+01:00

The simplified expression for the fraction is [tex]\frac{2(3x - 7) + 2x^3}{x^4}[/tex]

The complex fraction is given as:

((3x-7)/x^2)/(x^2/2)+(2/x)

Rewrite the fraction as product

((3x-7)/x^2)*(2/x^2)+(2/x)

Evaluate the product

[tex]\frac{2(3x - 7)}{x^4} + \frac 2x[/tex]

Take the LCM

[tex]\frac{2(3x - 7) + 2x^3}{x^4}[/tex]

Hence, the simplified expression for the fraction is [tex]\frac{2(3x - 7) + 2x^3}{x^4}[/tex]