Question

This is algebra 2. Would like an answer ASAP. Thanks! Between the two chunks of numbers, thats a division sign, not an addition sign.

Answer 1

Simplified form of
`(x+1)/(x^2+x-6)/ (x^2+5x+4)/(x-2)` is
`\mathbf{(1)/((x+3)(x+4)) }`

Option A is correct answer.

Explanation:

We need to find simplified form of
`(x+1)/(x^2+x-6)/ (x^2+5x+4)/(x-2)`

Solving the given expression:

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

First we find factors of
`x^2+x-6`

`x^2+x-6 \\= x^2+3x-2x-6\\= x(x+3)-2(x+3)\\=(x-2)(x+3)`

So, factors of
`x^2+x-6` are
`(x-2)(x+3)`

Now, fining the factors of
`x^2+5x+4`

`x^2+5x+4\\=x^2+4x+x+4\\=x(x+4)+1(x+4)\\=(x+1)(x+4)`

So, factors of
`x^2+5x+4` are
`(x+1)(x+4)\\`

Now the given expression will become:

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

Now, converting division sign into multiplication sign:

`=(x+1)/((x-2)(x+3))* \frac{x-2} {(x+1)(x+4)}\\Cancelling, \:common\:terms\\=(1)/((x+3)(x+4))`

So, simplified form of
`(x+1)/(x^2+x-6)/ (x^2+5x+4)/(x-2)` is
`\mathbf{(1)/((x+3)(x+4)) }`

Option A is correct answer.