Example 7: Combining rational expressions of the form 1/(ax) + 1/b, under the following conditions: a = b.

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Example 23: Combining rational expressions of the form 1/(x + a) - 1/(x + b), under the following conditions: a > 0, b > 0.

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Example 8: Combining rational expressions of the form 1/(ax) - 1/b, under the following conditions: a > 0, b > 0.

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Example 24: Combining rational expressions of the form 1/(x - a) - 1/(x + b), under the following conditions: a > 0, b > 0.

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Example 9: Combining rational expressions of the form a/(bx) + c/(dx), under the following conditions: a = c = 1, b > 0, d > 0.

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Example 25: Combining rational expressions of the form 1/(ax + b) + 1/(cx + d), under the following conditions: a = c =1, b > 0, d > 0.

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Example 10: Combining rational expressions of the form a/(bx) - c/(dx), under the following conditions: a = c = 1, b > 0, d > 0.

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Example 26: Combining rational expressions of the form 1/(ax - b) - 1/(cx - d), under the following conditions: a = c =1, b > 0, d > 0.

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Example 11: Combining rational expressions of the form a/(bx) + c/(dx), under the following conditions: a > 0, b > 0, c > 0, d > 0.

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Example 27: Combining rational expressions of the form 1/(ax - b) + 1/(cx + d), under the following conditions: a > 0, b > 0, c > 0, d > 0.

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Example 12: Combining rational expressions of the form a/(bx) - c/(dx), under the following conditions: a > 0, b > 0, c > 0, d > 0.

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Example 28: Combining rational expressions of the form 1/(ax + b) - 1/(cx + d), under the following conditions: a > 0, b > 0, c > 0, d > 0.

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Example 13: Combining rational expressions of the form 1/(x + a) + 1/b, under the following conditions: a = 1, b > 0.

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Example 14: Combining rational expressions of the form 1/(x + a) - 1/b, under the following conditions: a > 0, b > 0.

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Example 15: Combining rational expressions of the form 1/(x - a) + 1/b, under the following conditions: a > 0, b > 0.

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Example 16: Combining rational expressions of the form 1/(x - a) + 1/b, under the following conditions: a > 0, b > 0.

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Example 1: Combining rational expressions of the form 1/a + 1/b.

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Example 17: Combining rational expressions of the form 1/(x - a) - 1/b, under the following conditions: a > 0, b > 0.

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Example 2: Combining rational expressions of the form 1/a - 1/b.

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Example 18: Combining rational expressions of the form 1/(x + a) + 1/(x + b), under the following conditions: a > 0, b > 0.

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Example 3: Combining rational expressions of the form 1/(ax) + 1/b, under the following conditions: a = 1, b > 0.

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Example 19: Combining rational expressions of the form 1/(x + a) - 1/(x + b), under the following conditions: a > 0, b > 0.

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Example 4: Combining rational expressions of the form 1/(ax) - 1/b, under the following conditions: a = 1, b > 0.

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Example 20: Combining rational expressions of the form 1/(x - a) + 1/(x + b), under the following conditions: a > 0, b > 0.

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Example 5: Combining rational expressions of the form 1/(ax) + 1/b, under the following conditions: a > 0, b > 0.

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