Final answer:
To perform the indicated operations and simplify the expression, expand the fractions and find a common denominator. Combine like terms if possible.
Step-by-step explanation:
To perform the indicated operations and simplify the expression, let's start by simplifying the fractions. The first fraction is (6x^2)/(x^2-36)
Expanding the numerator using the distributive property, we get 6x^2 = 6x * x. The first fraction becomes (6x * x)/(x^2-36)
Next, we simplify the second fraction (6x)/(x-6). To simplify further, we multiply the numerator and denominator by the conjugate of the denominator, which is (x+6). The second fraction becomes (6x * (x+6))/((x-6) * (x+6))
Now we can combine the two fractions by finding a common denominator. The common denominator is (x^2 - 36) * (x+6). Multiplying the numerators and keeping the common denominator, we get (6x * x * (x+6))/(x^2-36)
Finally, we simplify the expression and combine like terms if possible.