Question

Simplify 1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+1).​

Answer 1

Answer:

$\frac{</strong><strong>3</strong><strong>}{ {</strong><strong>x^</strong><strong>2</strong><strong>}</strong><strong>+</strong><strong>4</strong><strong>x</strong><strong>+</strong><strong>3</strong><strong>} \:$

Step-by-step explanation:

$= > \frac{1}{(x + 1)(x + 2)} + \frac{1}{(x + 2)(x + 3)} + \frac{1}{(x + 3)(x + 1)} \\ \\ = > \frac{(x + 3)}{(x + 1)(x + 2)(x + 3)} + \frac{(x + 1)}{(x + 1)(x + 2)(x + 3)} + \frac{(x + 2)}{(x + 1)(x + 2)(x + 3)} \\ \\ = > \frac{(x + 1) + (x + 2) + (x + 3)}{(x + 1)(x + 2)(x + 3) } \\ \\ = > \frac{x + 1 + x + 2 + x + 3}{( </strong><strong>x</strong><strong>+</strong><strong>1</strong><strong>)</strong><strong>(</strong><strong>x</strong><strong>+</strong><strong>2</strong><strong>)(x + 3) } \\ \\ = > \frac{3</strong><strong>(</strong><strong>x</strong><strong> + </strong><strong>2</strong><strong>)</strong><strong>}{</strong><strong>(</strong><strong>x</strong><strong>+</strong><strong>1</strong><strong>)</strong><strong>(</strong><strong>x</strong><strong>+</strong><strong>2</strong><strong>)</strong><strong>(</strong><strong>x</strong><strong>+</strong><strong>3</strong><strong>)</strong><strong> } \\ \\ = > \frac{3</strong><strong>}{ </strong><strong>(</strong><strong>x</strong><strong>+</strong><strong>1</strong><strong>)</strong><strong>(</strong><strong>x</strong><strong>+</strong><strong>3</strong><strong>)</strong><strong>} \\ \\ = > \frac{3}{ </strong><strong>{</strong><strong>x^</strong><strong>2</strong><strong>}</strong><strong>+</strong><strong>4</strong><strong>x</strong><strong>+</strong><strong>3</strong><strong>}$