How do you multiply and simplify #\frac { b ^ { 2} - 81} { ( b - 9) ^ { 2} } \cdot \frac { 3b - 27} { 3b + 27} #?

1 Answer
Jim G.
Jun 28, 2017

#1#

Explanation:

#"factorise the numerators/denominators of the fractions"#

#b^2-81" is a "color(blue)"difference of squares"#

#rArrb^2-81=(b-9)(b+9)#

#rArr(b^2-81)/(b-9)^2xx(3b-27)/(3b+27)#

#=((b-9)(b+9))/((b-9)(b-9))xx(3(b-9))/(3(b+9))#

#"simplify by "color(blue)"cancelling common factors"#

#=(cancel((b-9))^1cancel((b+9))^1)/(cancel((b-9))^1cancel((b-9))^1)xx(cancel(3)cancel((b-9))^1)/(cancel(3)cancel((b+9))^1)#

#=1#

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