Question

Which expression is equivalent to the following complex fraction?

Answer 1

Answer:

Option (3) is correct.

The given expression $\dfrac{\frac{x}{x-3} }{\frac{x^2}{x^2-9} }$ is equivalent to $frac{x+3}{x}$

Step-by-step explanation:

Given expression $\dfrac{\frac{x}{x-3} }{\frac{x^2}{x^2-9} }$

We have to find an equivalent fraction to the given expression  $\dfrac{\frac{x}{x-3} }{\frac{x^2}{x^2-9} }$  out of given options.

Consider the given expression $\dfrac{\frac{x}{x-3} }{\frac{x^2}{x^2-9} }$

Divide fractions $\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a\cdot \:d}{b\cdot \:c}$

We have,

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

Cancelling common factor x, we have

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

Using algebraic identity $(a^2-b^2)=(a+b)(a-b)$, we have,

Apply on $x^2-9$ we get, $x^2-3^2=\left(x+3\right)\left(x-3\right)$

Substitute, we get,

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

Cancelling out common factor (x-3) , we get

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

Thus, the given expression $\dfrac{\frac{x}{x-3} }{\frac{x^2}{x^2-9} }$ is equivalent to $frac{x+3}{x}$

Option (3) is correct.

Answer 2

Answer:

x + 3/ x

which is the third option.

Answer: C)