How do you simplify #(w-3)/(w^2-w-20)+w/(w+4)#?

Question

Abigail Allen · Accepted Answer

#(w^2-4w-3)/((w-5)(w+4))#

Before we can add the fractions we require them to have a #color(blue)"common denominator"#

#"factorise the denominator of the left fraction"#

#rArr(w-3)/((w-5)(w+4))+w/(w+4)#

#"To obtain a common denominator"#

multiply the numerator/denominator of# w/(w+4)" by " (w-5)#

#rArr(w-3)/((w-5)(w+4))+(w(w-5))/((w-5)(w+4))#

Now we have a common denominator, add the numerators leaving the denominator as it is.

#rArr(w-3+w^2-5w)/((w-5)(w+4))#

#=(w^2-4w-3)/((w-5)(w+4))to(w!=5,w!=-4)#

Ethan Adkins · Answer

undefined To simplify the expression (w-3)/(w^2-w-20) + w/(w+4), we first need to find a common denominator. The common denominator for the two fractions is (w+4)(w-5).

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

[(w-3)(w+4)]/[(w+4)(w-5)] + [w(w-5)]/[(w+4)(w-5)]

Now, we can combine the fractions by adding the numerators:

[(w-3)(w+4) + w(w-5)]/[(w+4)(w-5)]

Expanding the brackets:

[(w^2 + w - 12 + w^2 - 5w)]/[(w+4)(w-5)]

Combining like terms:

[2w^2 - 4w - 12]/[(w+4)(w-5)]

Finally, we can simplify the expression further if possible. In this case, the expression cannot be simplified any further.