Question

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Answer 1

1).

$\frac{1}{3x} + \frac{3}{2x} - \frac{1}{x}$

$\frac{2 + 9 - 6}{6x}$

$\frac{5}{6x}$

2). a)

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

$\frac{x}{x - 1}$

b).

$\frac{12}{4{x}^{2} + 2x} = \frac{12}{2x(2x + 1)}$

$\frac{6}{x(2x + 1)}$

3). a)

$\frac{{x}^{2} - 16}{{x}^{2} + 8x + 16} = \frac{(x - 4)(x + 4)}{(x + 4)(x + 4)}$

$\frac{x - 4}{x + 4}$

b).

$\frac{{x}^{2} + 2x - 3}{{x}^{2} + 4x - 5} = \frac{(x +3)(x -1)}{(x + 5)(x - 1)}$

$\frac{x + 3}{x + 5}$

4).

$\frac{3}{x + 1} - \frac{2}{{x}^{2} - 1} + \frac{x}{x - 1}$

$\frac{3(x - 1) - 2 + x(x + 1)}{{x}^{2} - 1}$

$\frac{3x - 3 - 2 + {x}^{2} + x}{(x - 1)(x + 1)}$

$\frac{{x}^{2} + 4x - 5}{(x - 1)(x + 1)} = \frac{(x + 5)(x - 1)}{(x - 1)(x + 1)}$

$\frac{x + 5}{x + 1}$