How do you multiply and simplify #\frac { 25- y ^ { 2} } { y ^ { 2} + 8y + 15} \cdot \frac { y ^ { 2} + 8y + 12} { y ^ { 2} + y - 30}#?

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Answer 1 · 2017-11-28T18:47:16

#-((y+2))/((y+3))#

#\frac { 25- y ^ { 2} } { y ^ { 2} + 8y + 15} \cdot \frac { y ^ { 2} + 8y + 12} { y ^ { 2} + y - 30}" "larr# factorise first

#((5+y)(5-y))/((y+5)(y+3)) xx ((y+6)(y+2))/((y+6)(y-5))#

Now that you have all factors multiplied together you may cancel the like factors:

#(cancel((5+y))(5-y))/((cancel(y+5))(y+3)) xx (cancel((y+6))(y+2))/(cancel((y+6))(y-5))#

Multiply by #-1# in front of and inside a bracket to change the signs.

#color(red)(-(-5+y))/((y+3)) xx ((y+2))/((y-5))#

#=(-cancel((y-5)))/((y+3)) xx ((y+2))/cancel((y-5))#

#-((y+2))/((y+3))#