NelWashover
contestada

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

4 / x - 3

A.) x + 2 / x - 3 ÷ 4 / x + 2
B.) x + 2 / x - 3 · 4 / x + 2
C.) x + 2 / x - 3 - 4 / x + 2
D.) x + 2 / x - 3 + 4 / x + 2

Respuesta :

gmany

[tex] B.)\ \ \dfrac{4}{x-3}[/tex]

[tex]\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}[/tex]

carlosego

For this case we have the following expression:

[tex]\frac {4} {x-3}[/tex]

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

We have then:

[tex]\frac {4} {x-3} \frac {x + 2} {x + 2}[/tex]

Then, rewriting the given expression we have:

[tex]\frac {x + 2} {x-3} \frac {4} {x + 2}[/tex]

Answer:

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

[tex]\frac {x + 2} {x-3} \frac {4} {x + 2}[/tex]

Option B