Question

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

Answer 1

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.