Perform the following operation and express in simplest form. (x^(2)-12 x+35)/(x^(2)-25)÷(3x-21)/(8x+40) Answer:

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Perform the following operation and express in simplest form.  (x^(2)-12 x+35)/(x^(2)-25)÷(3x-21)/(8x+40) Answer:

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Identify and Rewrite Division: Identify the given expression and rewrite the division as multiplication by the reciprocal of the second fraction. $$(x^2-12x+35)/(x^2-25) ÷ (3x-21)/(8x+40) = (x^2-12x+35)/(x^2-25) * (8x+40)/(3x-21)$$Factor First Fraction: Factor the numerator and denominator of the first fraction. The numerator $x^2-12x+35$ can be factored into $(x-7)(x-5)$. The denominator $x^2-25$ is a difference of squares and can be factored into $(x+5)(x-5)$. So, the first fraction becomes $(x-7)(x-5)/(x+5)(x-5)$.Factor Second Fraction: Factor the numerator and denominator of the second fraction. The numerator $8x+40$ can be factored by taking out the common factor of 8, resulting in $8(x+5)$. The denominator $3x-21$ can be factored by taking out the common factor of 3, resulting in $3(x-7)$. So, the second fraction becomes $8(x+5)/3(x-7)$.Combine and Simplify: Combine the factored forms of the two fractions and simplify by canceling out common factors. $$((x-7)(x-5)/(x+5)(x-5)) * (8(x+5)/3(x-7))$$ The $(x-5)$ terms cancel out, as do the $(x-7)$ terms, and one $(x+5)$ term cancels out. This leaves us with $8/3$.Final Simplified Form: The final simplified form of the expression is $8/3$.

Perform the following operation and express in simplest form. $\newline$ $\frac{x^{2}-12 x+35}{x^{2}-25} \div \frac{3 x-21}{8 x+40}$ $\newline$ Answer:

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Perform the following operation and express in simplest form. $\newline$ $\frac{x^{2}-12 x+35}{x^{2}-25} \div \frac{3 x-21}{8 x+40}$ $\newline$ Answer: