Fully simplify the expression below and write your answer as a single fraction. (x^(4)-25x^(2))/(x^(2)+8x+15)*(x^(2)+2x-3)/(6x^(3)-36x^(2)+30 x) Answer:

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Fully simplify the expression below and write your answer as a single fraction.  (x^(4)-25x^(2))/(x^(2)+8x+15)*(x^(2)+2x-3)/(6x^(3)-36x^(2)+30 x) Answer:

Bytelearn · Accepted Answer

Factor Numerator and Denominator: First, factor the numerator and the denominator of both fractions where possible. The numerator of the first fraction, x^4 - 25x^2, can be factored as a difference of squares: (x^2 - 5^2)(x^2) = (x^2 - 25)(x^2). The denominator of the first fraction, x^2 + 8x + 15, can be factored as (x + 3)(x + 5). The numerator of the second fraction, x^2 + 2x - 3, can be factored as (x + 3)(x - 1). The denominator of the second fraction, 6x^3 - 36x^2 + 30x, can be factored by first taking out the common factor of 6x: 6x(x^2 - 6x + 5), and then factoring the quadratic: 6x(x - 5)(x - 1).Write Factored Expression: Now, write the expression with the factored terms: ((x^2 - 25)(x^2)) / ((x + 3)(x + 5)) * ((x + 3)(x - 1)) / (6x(x - 5)(x - 1)).Cancel Common Factors: Next, cancel out the common factors from the numerator and the denominator across the two fractions. The (x + 3) terms cancel out, as do the (x - 1) terms. Also, x^2 can be canceled with one of the x's in 6x. The expression now looks like this: ((x^2 - 25)x) / ((x + 5)) * (1) / (6(x - 5)).Simplify Expression: Simplify the expression further by canceling out the (x - 5) terms: ((x^2 - 25)x) / (6(x + 5)).Write Single Fraction: Finally, write the simplified expression as a single fraction: (x^3 - 25x) / (6x + 30).Further Simplify Fraction: We can simplify the fraction further by factoring out an x from the numerator and a 6 from the denominator: x(x^2 - 25) / 6(x + 5).Final Answer: Now, we can see that the expression is fully simplified and cannot be reduced further. The final answer is: x(x^2 - 25) / 6(x + 5).

Fully simplify the expression below and write your answer as a single fraction. $\newline$ $\frac{x^{4}-25 x^{2}}{x^{2}+8 x+15} \cdot \frac{x^{2}+2 x-3}{6 x^{3}-36 x^{2}+30 x}$ $\newline$ Answer:

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Fully simplify the expression below and write your answer as a single fraction.\newlinex4−25x2x2+8x+15⋅x2+2x−36x3−36x2+30x \frac{x^{4}-25 x^{2}}{x^{2}+8 x+15} \cdot \frac{x^{2}+2 x-3}{6 x^{3}-36 x^{2}+30 x} x2+8x+15x4−25x2​⋅6x3−36x2+30xx2+2x−3​\newlineAnswer:

Fully simplify the expression below and write your answer as a single fraction. $\newline$ $\frac{x^{4}-25 x^{2}}{x^{2}+8 x+15} \cdot \frac{x^{2}+2 x-3}{6 x^{3}-36 x^{2}+30 x}$ $\newline$ Answer: