Question

Which expression is equivalent to the following complex fraction? X/x-3/x^2/x^2-9

A) x-3/x
B) x+3/1
C) x+3/x
D) x/x+3

Answer 1

Answer:

C) $\frac{x+3}{x}$

Step-by-step explanation:

The given expression is

$\frac{\frac{x}{x-3} }{\frac{x^2}{x^2-9} }$

We rewrite to obtain:

$\frac{x}{x-3} \div \frac{x^2}{x^2-9}$

Multiply the first fraction by the reciprocal of the second to get;

$\frac{x}{x-3} \times \frac{x^2-9}{x^2}$

Factor the numerator using difference two squares;

$\frac{x}{x-3} \times \frac{x^2-3^2}{x^2}$

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

Cancel out the common factors to get;

$\frac{1}{1} \times \frac{(1)(x+3)}{x}$

This simplifies to;

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

Answer 2

Answer:

c

Step-by-step explanation: