1. Tính tích đầu tiên: \(\frac{4 \cdot 2}{(x+2)(x-2)} = \frac{8}{x^2-4}\)
2. Đổi dấu phân thức thứ hai: \(\frac{5x-6}{4-x^2} = -\frac{5x-6}{x^2-4}\)
3. Cùng mẫu số: \(\frac{8 - (5x-6)}{x^2-4} = \frac{8 - 5x + 6}{x^2-4} = \mathbf{\frac{14-5x}{x^2-4}}\)

1. Đổi dấu phân thức cuối: \(\frac{2}{2-x} = -\frac{2}{x-2}\)
2. Mẫu thức chung (MTC): \((x-2)(x+2) = x^2-4\)
3. Quy đồng và rút gọn:
   \(\frac{x^{2}+(x+2)-2(x+2)}{x^{2}-4}=\frac{x^{2}+x+2-2x-4}{x^{2}-4}=\frac{x^{2}-x-2}{x^{2}-4}\)
4. Phân tích tử thức: \(x^2 - x - 2 = (x-2)(x+1)\)
5. Kết quả: \(\frac{(x-2)(x+1)}{(x-2)(x+2)} = \mathbf{\frac{x+1}{x+2}}\)

1. MTC: \(a^2-1 = (a-1)(a+1)\)
2. Quy đồng:
   \(\frac{a^{2}(a-1)+(a+1)-2a}{a^{2}-1}=\frac{a^{3}-a^{2}+a+1-2a}{a^{2}-1}=\frac{a^{3}-a^{2}-a+1}{a^{2}-1}\)
3. Phân tích tử thức bằng cách nhóm:
   \(a^{2}(a-1)-(a-1)=(a^{2}-1)(a-1)\)
4. Kết quả: \(\frac{(a^2-1)(a-1)}{a^2-1} = \mathbf{a-1}\)

1. Đổi dấu: \(\frac{2}{2-x} = -\frac{2}{x-2}\)
2. MTC: \((x-2)(x+2)\)
3. Quy đồng:
   \(\frac{(x-2)-2(x+2)+x}{(x-2)(x+2)}=\frac{x-2-2x-4+x}{(x-2)(x+2)}=\frac{\mathbf{-6}}{\mathbf{x}^{\mathbf{2}}\mathbf{-4}}\)

1. Đổi dấu phân thức cuối: \(-\frac{2x(1-x)}{9-x^2} = +\frac{2x(1-x)}{x^2-9}\)
2. MTC: \(x^2-9 = (x-3)(x+3)\)
3. Quy đồng:
   \(\frac{(x+1)(x+3)-(1-x)(x-3)+2x(1-x)}{x^{2}-9}\)
4. Khai triển tử thức:
5. • \((x+1)(x+3) = x^2 + 4x + 3\)
   • \((1-x)(x-3) = x - 3 - x^2 + 3x = -x^2 + 4x - 3\)
   • \(2x(1-x) = 2x - 2x^2\)
6. Rút gọn tử thức:
   \((x^{2}+4x+3)-(-x^{2}+4x-3)+(2x-2x^{2})=x^{2}+4x+3+x^{2}-4x+3+2x-2x^{2}=2x+6\)
7. Kết quả: \(\frac{2x+6}{(x-3)(x+3)} = \frac{2(x+3)}{(x-3)(x+3)} = \mathbf{\frac{2}{x-3}}\)

6) ĐKXĐ: x+2≠0

=> x≠-2

x-2≠0

=>x≠2

\(4-x^2\ne0\)

\(x^2\ne4\)

=> x≠2 hoặc x≠-2

\(\frac{4}{x+2}\cdot\frac{2}{x-2}+\frac{\left(5x-6\right)}{4-x^2}\)

\(=\frac{8}{\left(x+2\right)\left(x-2\right)}-\frac{\left(5x-6\right)}{x^2-4}\)

\(=\frac{\left(-5x+14\right)}{\left(x+2\right)\left(x-2\right)}\)

7) ĐKXĐ: x≠-2 và x≠2

\(\frac{x^2}{x^2-4}+\frac{1}{x-2}+\frac{2}{2-x}\)

= \(\frac{x^2}{x^2-4}+\frac{1}{x-2}-\frac{2}{x-2}\)

\(=\frac{x^2}{x^2-4}-\frac{1}{x-2}\)

\(=\frac{x^2}{x^2-4}-\frac{\left(x+2\right)}{x^2-4}\)

\(=\frac{\left(x^2-x-2\right)}{\left(x-2\right)\left(x+2\right)}\)

= \(\frac{\left(x+1\right)\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}\)

= \(\frac{x+1}{x+2}\)

8) ĐKXĐ: a≠-1 và a≠1

\(\frac{a^2}{a+1}+\frac{1}{a-1}-\frac{2a}{a^2-1}\)

\(=\frac{a^2\left(a-1\right)+\left(a+1\right)}{\left(a+1\right)\left(a-1\right)}-\frac{2a}{\left(a-1\right)\left(a+1\right)}\)

\(=\frac{\left(a^3-a^2+a+1-2a\right)}{\left(a+1\right)\left(a-1\right)}\)

\(=\frac{\left(a^3-a^2-a+1\right)}{\left(a+1\right)\left(a-1\right)}\)

\(=\frac{a^2\left(a-1\right)-\left(a-1\right)}{\left(a+1\right)\left(a-1\right)}\)

\(=\frac{\left(a-1\right)\left(a^2-1\right)}{\left(a+1\right)\left(a-1\right)}\)

\(=a-1\)

9) ĐKXĐ:x≠-2 và x≠2

\(\frac{1}{x+2}+\frac{2}{2-x}+\frac{x}{x^2-4}\)

= \(\frac{1}{x+2}-\frac{2}{x-2}+\frac{x}{x^2-4}\)

\(=\frac{\left(x-2\right)-2\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}+\frac{x}{x^2-4}\)

\(=\frac{\left(x-2-2x-4+x\right)}{\left(x-2\right)\left(x+2\right)}\)

\(=-\frac{6}{\left(x-2\right)\left(x+2\right)}\)

10) ĐKXĐ: x≠3 hoặc x≠-3

\(\frac{\left(x+1\right)}{x-3}-\frac{\left(1-x\right)}{x+3}-\frac{2x\left(1-x\right)}{9-x^2}\)

\(=\frac{\left(x+1\right)\left(x+3\right)-\left(x-3\right)\left(1-x\right)}{\left(x-3\right)\left(x+3\right)}+\frac{2x\left(1-x\right)}{x^2-9}\)

\(=\frac{x^2+4x+3+\left(x-3\right)\left(x-1\right)}{\left(x-3\right)\left(x+3\right)}+\frac{2x\left(1-x\right)}{x^2-9}\)

\(=\frac{x^2+4x+3+\left(x^2-4x+3\right)}{\left(x-3\right)\left(x+3\right)}+\frac{2x-2x^2}{x^2-9}\)

\(=\frac{\left(2x^2+6+2x-2x^2\right)}{\left(x-3\right)\left(x+3\right)}\)

\(=\frac{\left(2x+6\right)}{\left(x-3\right)\left(x+3\right)}\)

\(=\frac{2\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}\)

\(=\frac{2}{x-3}\)

6: \(\frac{4}{x+2}-\frac{2}{x-2}+\frac{5x-6}{4-x^2}\)

\(=\frac{4}{x+2}-\frac{2}{x-2}-\frac{5x-6}{\left(x-2\right)\left(x+2\right)}\)

\(=\frac{4\left(x-2\right)-2\left(x+2\right)-5x+6}{\left(x-2\right)\left(x+2\right)}=\frac{4x-8-2x-4-5x+6}{\left(x-2\right)\left(x+2\right)}\)

\(=\frac{-3x-6}{\left(x-2\right)\left(x+2\right)}=\frac{-3\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}=\frac{-3}{x-2}\)

7: \(\frac{x^2}{x^2-4}+\frac{1}{x-2}+\frac{2}{2-x}\)

\(=\frac{x^2}{\left(x-2\right)\left(x+2\right)}-\frac{1}{x-2}=\frac{x^2-x-2}{\left(x-2\right)\left(x+2\right)}\)

\(=\frac{\left(x-2\right)\left(x+1\right)}{\left(x-2\right)\left(x+2\right)}=\frac{x+1}{x+2}\)

8: \(\frac{a^2}{a+1}+\frac{1}{a-1}-\frac{2a}{a^2-1}\)

\(=\frac{a^2\left(a-1\right)+a+1-2a}{\left.\left(a-1\right)\left(a+1\right)\right.}\)

\(=\frac{a^2\left(a-1\right)-\left(a-1\right)}{\left(a-1\right)\left(a+1\right)}=\frac{\left(a^2-1\right)\left(a-1\right)}{\left(a^2-1\right)}=a-1\)

9: \(\frac{1}{x+2}+\frac{2}{2-x}+\frac{x}{x^2-4}\)

\(=\frac{x-2}{\left(x+2\right)\left(x-2\right)}-\frac{2\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}+\frac{x}{\left(x-2\right)\left(x+2\right)}\)

\(=\frac{2x-2-2x-4}{\left(x-2\right)\left(x+2\right)}=-\frac{6}{x^2-4}\)

10: \(\frac{x+1}{x-3}-\frac{1-x}{x+3}-\frac{2x\left(1-x\right)}{9-x^2}\)

\(=\frac{x+1}{x-3}+\frac{x-1}{x+3}-\frac{2x\left(x-1\right)}{\left.\left(x-3\right)\left(x+3\right)\right.}\)

\(=\frac{\left(x+1\right)\left(x+3\right)+\left(x-1\right)\left(x-3\right)-2x\left(x-1\right)}{\left(x-3\right)\left(x+3\right)}\)

\(=\frac{x^2+4x+3+x^2-4x+3-2x^2+2x}{\left(x-3\right)\left(x+3\right)}=\frac{2x+6}{\left(x-3\right)\left(x+3\right)}\)

\(=\frac{2\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}=\frac{2}{x-3}\)