Algebra I question

Question

a divided by 2 times a-3 minus 5 divided by a squared - 9

 

        a                -                     5

    2(a-3)                              a^2-9

Answer 1

Begin by factoring the denominators to determine the common denominator

a/[2(a - 3)] - 5/[(a - 3)(a + 3)]

The common denominator is 2(a - 3)(a + 3), so multiply the first term by (a + 3)/(a + 3) and the second term by 2/2

(a + 3)/(a + 3) * a/[2(a - 3)] - 2/2 * 5/[(a -3)(a + 3)]

Next, multiply the numerators of your fractions and the denominators of your fractions

(a² + 3a)/[2(a - 3)(a + 3)] - 10/[(2(a - 3)( a + 3)]

Since you have common denominators, you can now combine the numerators over the common denominator

(a² + 3a - 10)/[2(a - 3)(a + 3)]

Factoring the numerator produces

[(a + 5)(a - 2)]/[2(a - 3)(a + 3)]

Since there are no common factors of the numerator and denominator, the answer cannot be reduced.  You can multiply the factors together to produce

(a² + 3a - 10)/(2a² - 18)