Fully simplify the expression below and write your answer as a single fraction. (x^(2)+5x)/(x^(2)+4x+3)*(4x^(2)-4)/(6x^(2)+24 x-30) Answer:

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Fully simplify the expression below and write your answer as a single fraction.  (x^(2)+5x)/(x^(2)+4x+3)*(4x^(2)-4)/(6x^(2)+24 x-30) Answer:

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Factorize fractions: Factor the numerator and denominator of both fractions where possible. The first fraction is (x^2 + 5x) / (x^2 + 4x + 3). We can factor the numerator by taking out the common factor x, and the denominator can be factored as a sum of squares. x(x + 5) / ((x + 1)(x + 3)) The second fraction is (4x^2 - 4) / (6x^2 + 24x - 30). We can factor out the common factor 4 in the numerator and factor the denominator. 4(x^2 - 1) / (6(x^2 + 4x - 5)) Now, notice that x^2 - 1 is a difference of squares and can be factored further. 4((x + 1)(x - 1)) / (6(x^2 + 4x - 5))Factorize second fraction: Factor the denominator of the second fraction. We need to factor 6(x^2 + 4x - 5). To do this, we look for two numbers that multiply to -30 (6 * -5) and add to 4. These numbers are 6 and -5. So, the factored form of the denominator is: 6((x + 6)(x - 5)) Now we can rewrite the second fraction as: 4((x + 1)(x - 1)) / (6(x + 6)(x - 5))Multiply fractions: Combine the two fractions by multiplying them. (x(x + 5) / ((x + 1)(x + 3))) * (4((x + 1)(x - 1)) / (6(x + 6)(x - 5))) To multiply fractions, we multiply the numerators together and the denominators together. (x(x + 5) * 4((x + 1)(x - 1))) / (((x + 1)(x + 3)) * (6(x + 6)(x - 5)))Cancel common factors: Cancel out common factors. We can cancel out the (x + 1) term that appears in both a numerator and a denominator. (x(x + 5) * 4(x - 1)) / ((x + 3) * (6(x + 6)(x - 5)))Simplify expression: Simplify the expression. Now we multiply out the remaining terms. (4x^2 + 20x) * (4(x - 1)) / ((x + 3) * (6(x + 6)(x - 5))) We can distribute the 4 in the numerator: (16x^2 - 16x) / ((x + 3) * (6(x + 6)(x - 5)))Multiply denominator terms: Simplify the expression further. We can now multiply the terms in the denominator: (16x^2 - 16x) / (6(x^2 + 6x - 5x - 30)) Simplify the terms in the denominator: (16x^2 - 16x) / (6(x^2 + x - 30))Reduce common factors: Simplify the expression by reducing common factors. We can divide both the numerator and the denominator by 2: (8x^2 - 8x) / (3(x^2 + x - 30))Check for further simplification: Check if the expression can be simplified further. The numerator and denominator do not have any common factors left, and the denominator cannot be factored in a way that would cancel out with the numerator. Therefore, the expression is fully simplified.

Fully simplify the expression below and write your answer as a single fraction. $\newline$ $\frac{x^{2}+5 x}{x^{2}+4 x+3} \cdot \frac{4 x^{2}-4}{6 x^{2}+24 x-30}$ $\newline$ Answer:

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Fully simplify the expression below and write your answer as a single fraction. $\newline$ $\frac{x^{2}+5 x}{x^{2}+4 x+3} \cdot \frac{4 x^{2}-4}{6 x^{2}+24 x-30}$ $\newline$ Answer: