How do you simplify #(3w)/(w^2-36) + w/(w-6)#?

Question

Genesis Allen · Accepted Answer

#\frac{x^2+9x}{x^2-36}# We have to find the lowest common denominator. We can see that #w-6# is a factor of #w^2-36#. If we multiply the top and bottom of #w/{w-6}# by #w+6# we get the following #\frac{3w}{w^2-36}+\frac{w(w+6)}{(w-6)(w+6)}# #\frac{3w}{w^2-36}+\frac{w^2+6w}{w^2-36}# #\frac{3w+w^2+6w}{w^2-36}# #\frac{w^2+9w}{w^2-36}#

Kennedy Adams · Answer

undefined To simplify the expression (3w)/(w^2-36) + w/(w-6), we first need to find a common denominator. The common denominator for the two fractions is (w-6)(w+6).

Next, we can rewrite the fractions with the common denominator:

(3w)/(w^2-36) + w/(w-6) = (3w)/(w^2-36) * (w+6)/(w+6) + w/(w-6) * (w+6)/(w+6)

Expanding the numerators, we get:

(3w(w+6))/(w^2-36) + w(w+6)/(w-6)(w+6)

Combining the fractions, we have:

(3w(w+6) + w(w+6))/(w^2-36)

Simplifying the numerator:

(3w^2 + 18w + w^2 + 6w)/(w^2-36)

Combining like terms:

(4w^2 + 24w)/(w^2-36)

Factoring out a common factor of 4w:

(4w(w + 6))/(w^2-36)

Finally, we can simplify further by factoring the denominator:

(4w(w + 6))/((w-6)(w+6))

Therefore, the simplified expression is (4w(w + 6))/((w-6)(w+6)).