multiply and simplify (x^2+x-12/x-3)*(x^2-2x-3/x^2+5x+4)
((x2 + x - 12)/(x - 3))·((x2 - 2x - 3)/(x2 + 5x + 4))
First, if possible, factor the polynomial(s) in each rational expression:
(x2 + x - 12)/(x - 3) = ((x + 4)(x - 3))/(x - 3)
Notice that in this rational expression there is a common factor in both the numerator and the denominator, that being 'x - 3'. With that, these 2 factors cancel each other out.
((x + 4)(x - 3))/(x - 3) = (x + 4)
For the second rational expression,
(x2 - 2x - 3)/(x2 + 5x + 4) = ((x + 1)(x - 3))/((x + 1)(x + 4))
Common factor in both numerator and denominator here is 'x + 1'
((x + 1)(x - 3))/((x + 1)(x + 4)) = (x - 3)/(x + 4)
Substitute the simplified forms of the rational expressions into the original problem:
((x2 + x - 12)/(x - 3))·((x2 - 2x - 3)/(x2 + 5x + 4))
= (x + 4)·((x - 3)/(x + 4))
= ((x + 4)(x - 3))/(x + 4)
After multiplying the simplified forms of the rational expressions, we see that there is another common factor in both the numerator and the denominator that cancels out, that being 'x + 4'. And that leaves us with the final solution:
((x + 4)(x - 3))/(x + 4) = (x - 3)