How do you simplify #\frac { x - 2} { 25x - 25} \cdot \frac { 5} { x ^ { 2} - 4}#?

1 Answer
Jan 18, 2018

#color(blue)(1/(5*(x-1)*(x+2))#

Explanation:

Given:

#\frac { x - 2} { 25x - 25} \cdot \frac { 5} { x ^ { 2} - 4}#

#rArr (x-2)/(25(x-1))*5/((x+2)(x-2))#

#rArr cancel (x-2)/(25(x-1))*5/((x+2) cancel ((x-2))#

#rArr (5/25)(1/((x-1)*(x+2)))#

#rArr 1/(5(x-1)*(x+2))#

Hence,

#\frac { x - 2} { 25x - 25} \cdot \frac { 5} { x ^ { 2} - 4} = 1/(5(x-1)*(x+2))#