Question

What is the simplified form of x plus 4 over x squared plus x minus 12 ⋅ x plus 4 over x squared plus 8x plus 16 ?

1 over the quantity x minus 4 squared
1 over the quantity x plus 3 times the quantity x minus 4
1 over the quantity x plus 4 squared
1 over the quantity x minus 3 times the quantity x plus 4

Answer 1

The correct option is 4.

Explanation:

The given expression is,

`(x+4)/(x^2+x-12) \cdot (x+4)/(x^2+8x+16)`

Use grouping method to factorize the denominations.

`(x+4)/(x^2+4x-3x-12) \cdot (x+4)/(x^2+4x+4x+16)`

`(x+4)/(x(x+4)-3(x+4)) \cdot (x+4)/(x(x+4)+4(x+4))`

`(x+4)/((x+4)(x-3)) \cdot (x+4)/((x+4)(x+4))`

Cancel out the common factor (x+4).

`(1)/(x-3) \cdot (1)/(x+4)`

`(1)/((x-3)(x+4))`

Therefore the correct option is 4.