Question

Express the following as a fraction with a single denominator: 1/(2a-3) - 2/(3-2a) + 18/(9-4a^2)

Answer 1

Answer:

9-4a^2 can be factored into (3-2a)(3+2a)

(2a-3) = -1(3-2a)

So, your statement becomes -1/(3-2a) - 2/(3-2a) + 18/[(3-2a)(3+2a)].

Combining the first two, you get -3/(3-2a) + 18/[(3-2a)(3+2a)].

Multiplying the first part (top and bottom) by (3+2a), you get:

-3(3+2a)/[(3-2a)(3+2a)] + 18/[(3-2a)(3+2a)] = (-9-6a+18)/[(3-2a)(3+2a)] = (9-6a)/[(3-2a)(3+2a)]

The numerator can be factored to 3(3-2a), so we can cancel that from the numerator and denominator, leaving:

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