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

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

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))`