Question

Select the rational expression that is equivalent to the given expression below.

Answer 1

For this case we have the following expression:

$\frac {4} {x-3}$

We must multiply the expression given by the same factor in the numerator and the denominator.

We have then:

$\frac {4} {x-3} \frac {x + 2} {x + 2}$

Then, rewriting the given expression we have:

$\frac {x + 2} {x-3} \frac {4} {x + 2}$

Answer:

The rational expression that is equivalent to the given expression is:

$\frac {x + 2} {x-3} \frac {4} {x + 2}$

Option B

Answer 2

$B.)\ \ \dfrac{4}{x-3}$

$\dfrac{x+2}{x-3}\cdot\dfrac{4}{x+2}\\\\=\dfrac{(x+2)(4)}{(x-3)(x+2)}\qquad\text{cancel}\ (x+2)\\\\=\dfrac{4}{x-3}$