To simplify the given expression, we need to factor each polynomial in the numerators and denominators. Once factored, we can cancel out any common factors between the numerators and denominators.
Step 1: Factor the Expressions
We start by factoring each polynomial in the expression:
x2−3x−4=(x−4)(x+1)
x2−6x+8=(x−4)(x−2)
x2−7x+10=(x−5)(x−2)
x2+5x+4=(x+1)(x+4)
Step 2: Rewrite the Expression
Substituting the factored forms into the original expression, we have:
(x−4)(x−2)(x−4)(x+1)⋅(x+1)(x+4)(x−5)(x−2)
Step 3: Cancel Common Factors
Next, we can cancel the common factors in the numerator and denominator: