How do you multiply and simplify #\frac { y ^ { 2} - 5y } { y ^ { 2} - 9} \cdot \frac { y + 3} { y - 5}#?

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Answer 1 · 2017-04-26T03:21:30

#y/(y-3)#

Given:#(y^2 - 5y)/(y^2 - 9) * (y+3)/(y - 5)#

Factor the terms on the left using GCF #2x^2-10x = 2x(x-5)# & the difference of squares #a^2 - b^2 = (a - b)(a + b)#:

#(y(y-5))/((y-3)(y+3)) * (y+3)/(y - 5)#

Multiplication can occur in any order:

#(y(y-5)(y+3))/((y-3)(y+3)(y - 5))#

Cancel factors that are common to both the numerator and denominator:

#(y cancel(y-5)color(red)cancel(y+3)) / ((y-3)color(red)cancel(y+3) cancel(y - 5))#

#= y/(y-3)#