Question

What is the simplified form of x-2 over x2+x-6 divided x2+5x+4 over x+4

Answer 1

x-2 over x2+x-6 divided x2+5x+4 over x+4 requires 2 factoring, canceling like factors, and inverting the divisor and multiplying.

(x-2) over (x+3)(x-2) divided by (x+4)(x+1) over (x+4) after factoring twice

canceling like factors
1 over (x+3) divided by (x+1) over 1
invert denominator and multiply

answer 1 over (x+3)(x+1)

 

Answer 2

Answer:

$1/((x+3)*(x+1))$

Step-by-step explanation:

We can write the expression as:

$((x-2)/(x^2+x-6))/((x^2+5*x+4)/(x+4))$

We can write the term as a single division by multiplying the terms in numerator by the inverse on the terms in the denominator:

$((x-2)/(x^2+x-6))*((x+4)/(x^2+5*x+4)/)$

$((x-2)*(x+4))/((x^2+x-6)*(x^2+5*x+4))$

We can simplfy the denominator terms as:

$x^2+x-6=(x+3)*(x-2)$

$x^2+5*x+4=(x+4)*(x+1)$

Therefore (x-2) and (x+4) in the numerator and denominator cancels out and we are left with:

$1/((x+3)*(x+1))$