Answer
$\frac{(2a-1)}{(3a-1)}$
Work Step by Step
Since the numerator and the denominator both consist of a trinomial, we use the rules of factoring trinomials in order to factor them. Then, we cancel out the resultant common factors in the numerator and the denominator:
$\frac{10a^{2}+a-3}{15a^{2}+4a-3}$
=$\frac{10a^{2}-5a+6a-3}{15a^{2}-5a+9a-3}$
=$\frac{5a(2a-1)+3(2a-1)}{5a(3a-1)+3(3a-1)}$
=$\frac{(2a-1)(5a+3)}{(3a-1)(5a+3)}$
=$\frac{(2a-1)}{(3a-1)}$
