Answer: (5a+b)/2
Step-by-step explanation:
1. First factor 5a^2+36ab+7b^2
=(5a+b)(a+7b)
2. Factor 2a+14b
The two can be factored out, making the equation equal to 2(a+7b).
The factored out equation is now [tex]\frac{(5a+b)(a+7b)}{2(a+7b)}[/tex]
Since there is an (a+7b) on both sides of the fraction, they cancel out. You are left with (5a+b)/2. This fraction cannot be simplified more.
To verify you can multiply (5a+b)/2 times (2a+14b). If it is correct, it should come back out as 5a^2 + 36ab +7b^2
