mplify the expression below and write your answe (x^(2)+10 x)/(x(x+10)^(2))*((x+10)^(2))/(x^(2)+19 x+90)

Write Expression: Write down the expression to be simplified. (x^2 + 10x) / (x(x + 10)^2) * ((x + 10)^2) / (x^2 + 19x + 90)Factor Denominator: Factor the denominator of the second fraction if possible. x^2 + 19x + 90 can be factored into (x + 10)(x + 9). So, the expression becomes: (x^2 + 10x) / (x(x + 10)^2) * ((x + 10)^2) / ((x + 10)(x + 9))Cancel Common Factors: Cancel out common factors from the numerator and the denominator. The (x + 10)^2 in the numerator cancels with one (x + 10) in the denominator and the remaining (x + 10) in the numerator. The x in the denominator of the first fraction cancels with the x in the numerator of the second fraction. The expression simplifies to: (x^2 + 10x) / (x(x + 10)) * 1 / (x + 9) =(x(x + 10)) / (x(x + 10)) * 1 / (x + 9) =1 * 1 / (x + 9) =1 / (x + 9)Final Simplified Expression: Write down the final simplified expression. The final simplified expression is 1 / (x + 9).

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Algebra 2

Simplify rational expressions

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Q. Simplify the expression below and write your answer in simplest form:

\newline

\frac{x^{2}+10x}{x(x+10)^{2}} \cdot \frac{(x+10)^{2}}{x^{2}+19x+90}

Write Expression: Write down the expression to be simplified. $\newline$ $(x^2 + 10x) / (x(x + 10)^2) \times ((x + 10)^2) / (x^2 + 19x + 90)$
Factor Denominator: Factor the denominator of the second fraction if possible. $\newline$ $x^2 + 19x + 90$ can be factored into $(x + 10)(x + 9)$ . $\newline$ So, the expression becomes: $\newline$ $\frac{x^2 + 10x}{x(x + 10)^2} \times \frac{(x + 10)^2}{(x + 10)(x + 9)}$
Cancel Common Factors: Cancel out common factors from the numerator and the denominator. $\newline$ The $(x + 10)^2$ in the numerator cancels with one $(x + 10)$ in the denominator and the remaining $(x + 10)$ in the numerator. $\newline$ The $x$ in the denominator of the first fraction cancels with the $x$ in the numerator of the second fraction. $\newline$ The expression simplifies to: $\newline$ $(x^2 + 10x) / (x(x + 10)) \times 1 / (x + 9)$ $\newline$ $=(x(x + 10)) / (x(x + 10)) \times 1 / (x + 9)$ $\newline$ $=1 \times 1 / (x + 9)$ $\newline$ $=1 / (x + 9)$
Final Simplified Expression: Write down the final simplified expression. $\newline$ The final simplified expression is $\frac{1}{(x + 9)}$ .