Simplify the expression: (x^(2)+25)/(x^(2)-10 x+25)

Identify function: Identify the function to differentiate. Function: (x^(2)+25)/(x^(2)-10x+25)Apply quotient rule: Apply the quotient rule: (v'u - uv') / v^2. Let u = x^2 + 25 and v = x^2 - 10x + 25. Then, du/dx = 2x and dv/dx = 2x - 10.Substitute into formula: Substitute into the quotient rule formula. (d/dx) = [(x^2 - 10x + 25)(2x) - (x^2 + 25)(2x - 10)] / (x^2 - 10x + 25)^2Expand and simplify: Expand and simplify the numerator. Numerator = (2x^3 - 20x^2 + 50x) - (2x^3 - 10x^2 - 50x + 250) = -10x^2 + 100x + 250

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Simplify the expression: (x^(2)+25)/(x^(2)-10 x+25)

Simplify the expression: $\frac{x^{2}+25}{x^{2}-10x+25}$

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Q. Simplify the expression:

\frac{x^{2}+25}{x^{2}-10x+25}

Identify function: Identify the function to differentiate. $\newline$ Function: $(x^{2}+25)/(x^{2}-10x+25)$
Apply quotient rule: Apply the quotient rule: $(v'u - uv') / v^2$ . Let $u = x^2 + 25$ and $v = x^2 - 10x + 25$ . Then, $du/dx = 2x$ and $dv/dx = 2x - 10$ .
Substitute into formula: Substitute into the quotient rule formula. $\newline$ $(\frac{d}{dx}) = \frac{(x^2 - 10x + 25)(2x) - (x^2 + 25)(2x - 10)}{(x^2 - 10x + 25)^2}$
Expand and simplify: Expand and simplify the numerator. $\newline$ Numerator = $2x^3 - 20x^2 + 50x$ - $2x^3 - 10x^2 - 50x + 250$ $\newline$ = (-10\)x^ $2$ + $100$ x + $250$