Question #f78ff

1 Answer
Mar 13, 2017

Answer:

#(y^2 + 11y + 30)/(y + 5) = y + 6#

Explanation:

Given: #(y^2 + 11y + 30)/(y + 5)#

Can be solved by reducing the numerator (top bracket) to see how it will react with the denominator (bottom bracket).

We have #(y^2 + 11y + 30)# that we know can be factored into two terms containing #y# because the #y# exponent is #2#.

#(y#....... #)# #(y#....... #)#

Looking at the 30, we see it can be factored into #2 xx 15#; or #10 xx 3#; or #5 xx 6#.
The last factors look appealing because they will add up to #11# to match the given middle term.

Now: #(y#....... #5#)# #(y#....... #6#)#

And we know both signs here must be positive because we had to #add# #5# to #6# to get the #11#.

Then: #(y + 5#)# #(y# + 6)#

Placing our factors into the original equation:

#[(y + 5)(y + 6)]/ (y+5)#

Gives us good news, because one of the factors cancels out the denominator to leave:

#1(y + 6) = (y + 6)#

#(y^2 + 11y + 30)/(y + 5) = y + 6#