Fully simplify the expression below and write your answer as a single fraction. (2x^(4)-8x^(2))/(x^(4)-10x^(3))*(x+7)/(4x^(2)+36 x+56) Answer:

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Fully simplify the expression below and write your answer as a single fraction.  (2x^(4)-8x^(2))/(x^(4)-10x^(3))*(x+7)/(4x^(2)+36 x+56) Answer:

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Factor Numerator and Denominator: First, factor the numerator and the denominator of the first fraction. The numerator 2x^4 - 8x^2 can be factored by taking out the common factor of 2x^2, resulting in 2x^2(x^2 - 4). The denominator x^4 - 10x^3 can be factored by taking out the common factor of x^3, resulting in x^3(x - 10).Factor Second Fraction: Now, factor the numerator and the denominator of the second fraction. The numerator x + 7 is already in its simplest form. The denominator 4x^2 + 36x + 56 can be factored by grouping. We can factor out a 4, resulting in 4(x^2 + 9x + 14). Then, we can factor the quadratic as 4(x + 2)(x + 7).Combine and Cancel Common Factors: Combine the factored forms of the numerator and denominator to rewrite the original expression. The expression becomes (2x^2(x^2 - 4))/(x^3(x - 10)) * (x + 7)/(4(x + 2)(x + 7)).Simplify Expression: Next, we can cancel out common factors from the numerator and the denominator across the fractions. The (x + 7) terms cancel each other out. We are left with (2x^2(x^2 - 4))/(x^3(x - 10)) * 1/(4(x + 2)).Recognize Difference of Squares: Now, we can simplify the expression further by canceling out any common factors. The x^2 term in the numerator can cancel out two x's from the x^3 term in the denominator. We are left with (2(x^2 - 4))/(x(x - 10)) * 1/(4(x + 2)).Substitute Factored Form: We can now simplify the expression (x^2 - 4) by recognizing it as a difference of squares. The expression x^2 - 4 can be factored into (x + 2)(x - 2).Cancel Common Terms: Substitute the factored form of x^2 - 4 into the expression. We now have (2(x + 2)(x - 2))/(x(x - 10)) * 1/(4(x + 2)).Combine Remaining Factors: Cancel out the common (x + 2) terms from the numerator and the denominator. We are left with (2(x - 2))/(x(x - 10)) * 1/4.Final Simplified Expression: Combine the remaining factors to form a single fraction. The expression simplifies to (2(x - 2))/(4x(x - 10)).Finally, we can simplify the fraction by dividing both the numerator and the denominator by 2. The final simplified expression is (x - 2)/(2x(x - 10)).

Fully simplify the expression below and write your answer as a single fraction. $\newline$ $\frac{2 x^{4}-8 x^{2}}{x^{4}-10 x^{3}} \cdot \frac{x+7}{4 x^{2}+36 x+56}$ $\newline$ Answer:

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Fully simplify the expression below and write your answer as a single fraction.\newline2x4−8x2x4−10x3⋅x+74x2+36x+56 \frac{2 x^{4}-8 x^{2}}{x^{4}-10 x^{3}} \cdot \frac{x+7}{4 x^{2}+36 x+56} x4−10x32x4−8x2​⋅4x2+36x+56x+7​\newlineAnswer:

Fully simplify the expression below and write your answer as a single fraction. $\newline$ $\frac{2 x^{4}-8 x^{2}}{x^{4}-10 x^{3}} \cdot \frac{x+7}{4 x^{2}+36 x+56}$ $\newline$ Answer: