Question

Please help simplify the given expression

Answer 1

`(34(a+2))/(23(a-13))`

Explanation:

Realize that dividing by a fraction is the same as multiplying by its inverse. Then factor the expressions and cancel common factors from numerator and denominator.

`\displaystyle(\left((2(a^2+5a+6))/(5(a^2-169))\right))/(\left((23(a+3))/(85(a+13))\right))=(2(a^2+5a+6))/(5(a^2-169))\cdot(85(a+13))/(23(a+3))\\\\=(2\cdot 5\cdot 17(a+13)(a+3)(a+2))/(5\cdot 23(a+13)(a+3)(a-13))=(34(a+2))/(23(a-13))`