find the product
v^2+v-12/5v+10*-v-2/v^2+5v+4
To find the product, we need to simplify and multiply the given expression. Let's break it down step by step:
1. Simplify the expression:
Start by factoring the numerator and the denominator separately.
Numerator: v^2 + v - 12 = (v - 3)(v + 4)
Denominator: 5v + 10 = 5(v + 2)
-v - 2 = -1(v + 2)
v^2 + 5v + 4 = (v + 1)(v + 4)
So, the expression becomes [(v - 3)(v + 4)] / [5(v + 2) * -1(v + 2)] / [(v + 1)(v + 4)]
2. Now simplify further:
We can cancel out the common factors between the numerators and denominators.
[(v - 3)(v + 4)] / [5(v + 2) * -1(v + 2)] / [(v + 1)(v + 4)] =
[(v - 3)] / [5 * -1] / [(v + 1)] =
-(v - 3) / 5(v + 1)
Now, we have simplified the expression.
3. State the product:
The product of the expression is -(v - 3) / 5(v + 1).