(5y+5)/(y^2^+7y+6)*(y^2^+4y-12)/(y^2^+3y-10)
Simplify
Leave answer in factored form. Keep () around binomial factors.
5(y+1)/((y+1)(y+6) * (y+6)(y-2)/((y+5)(y-2))
= y/(y+5) , y ≠ -1, -6, 2
To simplify the given expression, we need to factor each of the four polynomials involved and then cancel out any common factors in the numerator and denominator.
Let's start by factoring each polynomial:
1. Numerator 1: 5y + 5
We can factor out 5 from both terms: 5(y + 1)
2. Denominator 1: y^2 + 7y + 6
This is a quadratic polynomial, and we can factor it by finding two numbers whose sum is 7 and whose product is 6. In this case, the numbers are 2 and 3. Hence, we can rewrite the polynomial as (y + 3)(y + 2).
3. Numerator 2: y^2 + 4y - 12
Here, we need to find two numbers whose sum is 4 and whose product is -12. The numbers are 6 and -2. Thus, we can factor the polynomial as (y + 6)(y - 2).
4. Denominator 2: y^2 + 3y - 10
This quadratic polynomial can be factored by finding two numbers whose sum is 3 and whose product is -10. The numbers are 5 and -2. Hence, the factored form is (y + 5)(y - 2).
Now, let's substitute the factored forms back into the expression and cancel out any common factors:
(5(y + 1) / [(y + 3)(y + 2)]) * ([(y + 6)(y - 2)] / [(y + 5)(y - 2)])
Observe that (y - 2) appears both in the numerator and denominator, so we can cancel it out:
(5(y + 1) / [(y + 3)(y + 2)]) * [(y + 6) / (y + 5)]
And there you have it – the simplified form of the given expression in factored form.