Simplify: x/4x+x² A. 1/4 B. 1/4+x ; where x ≠ -4,0 C. 1/4+x ; where x ≠ -4 D. 1/4x ; where x ≠ 0

Question

asked Nov 2, 2020 65.2k views

1 Answer

Trevin Avery · Answer 1 · 2020-11-07T18:01:15+0000

ANSWER

B. 1/4+x ; where x ≠ -4,0

Step-by-step explanation

The given expression is:

$\frac{x}{4x + {x}^(2) }$

This expression is defined if and only if,

$(4x + {x}^(2) ) \\e 0$

$x(4 + x) \\e0$

$x\\e0 \: or \: x\\e - 4$

The greatest common factor in the denominator is x.

We factor the greatest common factor is

(x)/(x(4 + x))

Cancel the common factors to ontain;

(1)/(4+ x )

The correct choice is B.