Question

What is the simplified form of x plus 1 over x squared plus x minus 6 divided by x squared plus 5x plus 4 over x plus 4 ?

A. 1 over the quantity x plus 3 times the quantity x plus 4
B. 1 over the quantity x plus 3 times the quantity x minus 2
C. 1 over the quantity x plus 4 times the quantity x minus 2
D. 1 over the quantity x plus 3 times the quantity x plus 1

Answer 1

Option B is correct.

Explanation:

We have given an expression:

`(((x+1))/(x^2+x-6))/((x^2+5x+4)/((x+4)))`

After rearranging the terms from
`((a)/(b))/((c)/(d))=(a\cdot d)/(b\cdot c)`

We will get
`((x+1)(x+4))/((x^2+x-6)(x^2+5x+4))`

Now, we will simplify the terms

`((x+4)(x+1))/((x^2+3x-2x-6)(x^2+4x+x+4))`

After further simplification we will get

`((x+4)(x+1))/((x(x+3)-2(x+3))(x(x+4)+1(x+4)))`

Now, we will get

`((x+4)(x+1))/((x-2)(x+3)(x+1)(x+4))`

Now, cancel out the common terms from numerator and denominator which is (x+4)(x+1) we will get

`(1)/((x-2)(x+3))`

Therefore, Option B is correct.

Answer 2

x +1 x^2 +5x +4 x +1 (x +1)(x +4)
---------------- / ---------------------- = ----------------- / ----------------------- =
x^2 +x -6 x +4 (x +3)(x -2) x +4

x +1 1 1
= ---------------- * ----------- = ------------------
(x +3)(x -2) ( x +1) (x +3)(x -2)

so the second choice is right sure