How do you simplify #\frac { y } { y ^ { 2} + 8y + 15} + \frac { y - 1} { y ^ { 2} + 7y + 12}#?

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Answer 1 · 2016-10-23T15:29:55

#(2y^2+8y -5)/((y+3)(y+5)(y+4)#

When adding or subtracting fractions you need to have common denominator. (LCD)

Algebraic fractions are just the same. Before you can find a factor you often need to factorise the denominators first.

#y/color(blue)(y^2 +8y +15) + (y-1)/color(red)(y^2+7y +12)#

#color(blue)("find factors of 15 which add up to 8 "larr#3 and 5
#color(red)("find factors of 12 which add up to 7 "larr# 3 and 4

=#y/color(blue)((y+3)(y+5)) + y/color(red)((y+3)(y+4))#

=#(y(y+4) + (y-1)(y+5))/((y+3)(y+5)(y+4)larr LCD)#

=#(y^2+4y+ y^2+5y -y -5)/((y+3)(y+5)(y+4)#

=#(2y^2+8y -5)/((y+3)(y+5)(y+4)#