Hmaxant \( \begin{array}{lll}\text { (10) } \frac{27 p^{3}-8}{27 p^{2}+18 p+12} & \text { (11) } \frac{9-k^{2}}{k^{2}-3 k} & \text { (12) } \frac{6+9 k}{9 k^{2}-4} \\ \text { (13) } \frac{10-2 x}{x-5} & \text { (14) } \frac{x^{2}(x+2)-4(x+2)}{(x+2)^{2}} & \text { (15) } \frac{(3-1)^{2}}{x^{2}-9}\end{array} \)

Simplify the expression by following steps: - step0: Solution: \(\frac{\left(3-1\right)^{2}}{\left(x^{2}-9\right)}\) - step1: Remove the parentheses: \(\frac{\left(3-1\right)^{2}}{x^{2}-9}\) - step2: Subtract the numbers: \(\frac{2^{2}}{x^{2}-9}\) - step3: Evaluate the power: \(\frac{4}{x^{2}-9}\) Calculate or simplify the expression \( (9 - k^2)/(k^2 - 3*k) \). Simplify the expression by following steps: - step0: Solution: \(\frac{\left(9-k^{2}\right)}{\left(k^{2}-3k\right)}\) - step1: Remove the parentheses: \(\frac{9-k^{2}}{k^{2}-3k}\) - step2: Factor the expression: \(\frac{\left(k-3\right)\left(-3-k\right)}{k\left(k-3\right)}\) - step3: Reduce the fraction: \(\frac{-3-k}{k}\) - step4: Calculate: \(-\frac{3+k}{k}\) Calculate or simplify the expression \( (27*p^3 - 8)/(27*p^2 + 18*p + 12) \). Simplify the expression by following steps: - step0: Solution: \(\frac{\left(27p^{3}-8\right)}{\left(27p^{2}+18p+12\right)}\) - step1: Remove the parentheses: \(\frac{27p^{3}-8}{27p^{2}+18p+12}\) - step2: Factor the expression: \(\frac{\left(9p^{2}+6p+4\right)\left(3p-2\right)}{3\left(9p^{2}+6p+4\right)}\) - step3: Reduce the fraction: \(\frac{3p-2}{3}\) Calculate or simplify the expression \( (x^2*(x + 2) - 4*(x + 2))/((x + 2)^2) \). Simplify the expression by following steps: - step0: Solution: \(\frac{\left(x^{2}\left(x+2\right)-4\left(x+2\right)\right)}{\left(x+2\right)^{2}}\) - step1: Remove the parentheses: \(\frac{x^{2}\left(x+2\right)-4\left(x+2\right)}{\left(x+2\right)^{2}}\) - step2: Subtract the terms: \(\frac{x^{3}+2x^{2}-4x-8}{\left(x+2\right)^{2}}\) - step3: Factor the expression: \(\frac{\left(x+2\right)\left(x^{2}-4\right)}{\left(x+2\right)^{2}}\) - step4: Reduce the fraction: \(\frac{x^{2}-4}{x+2}\) - step5: Factor the expression: \(\frac{\left(x+2\right)\left(x-2\right)}{x+2}\) - step6: Reduce the fraction: \(x-2\) Calculate or simplify the expression \( (10 - 2*x)/(x - 5) \). Simplify the expression by following steps: - step0: Solution: \(\frac{\left(10-2x\right)}{\left(x-5\right)}\) - step1: Remove the parentheses: \(\frac{10-2x}{x-5}\) - step2: Factor the expression: \(\frac{-2\left(x-5\right)}{x-5}\) - step3: Reduce the fraction: \(-2\) Calculate or simplify the expression \( (6 + 9*k)/(9*k^2 - 4) \). Simplify the expression by following steps: - step0: Solution: \(\frac{\left(6+9k\right)}{\left(9k^{2}-4\right)}\) - step1: Remove the parentheses: \(\frac{6+9k}{9k^{2}-4}\) - step2: Factor the expression: \(\frac{3\left(3k+2\right)}{\left(3k+2\right)\left(3k-2\right)}\) - step3: Reduce the fraction: \(\frac{3}{3k-2}\) Here are the simplified results for each of the given expressions: 1. **Expression (10)**: \[ \frac{27 p^{3}-8}{27 p^{2}+18 p+12} \rightarrow \frac{3p-2}{3} \] 2. **Expression (11)**: \[ \frac{9-k^{2}}{k^{2}-3 k} \rightarrow -\frac{3+k}{k} \] 3. **Expression (12)**: \[ \frac{6+9 k}{9 k^{2}-4} \rightarrow \frac{3}{3k-2} \] 4. **Expression (13)**: \[ \frac{10-2 x}{x-5} \rightarrow -2 \] 5. **Expression (14)**: \[ \frac{x^{2}(x+2)-4(x+2)}{(x+2)^{2}} \rightarrow x-2 \] 6. **Expression (15)**: \[ \frac{(3-1)^{2}}{x^{2}-9} \rightarrow \frac{4}{x^{2}-9} \] These results provide the simplified forms of each expression. If you need further assistance or explanations, feel free to ask!