How do you solve #\frac { u - 2} { u - 5} + 1= \frac { u - 5} { u - 3}#?
1 Answer
Dec 11, 2017
Explanation:
Given:
#(u-2)/(u-5)+1 = (u-5)/(u-3)#
Multiply both sides by
#(u-2)(u-3)+(u-5)(u-3) = (u-5)^2#
Multiply out to get:
#(u^2-5u+6)+(u^2-8u+15) = u^2-10u+25#
Simplify the left hand side:
#2u^2-13u+21 = u^2-10u+25#
Subtract the right hand side from the left and transpose to get:
#0 = u^2-3u-4 = (u-4)(u+1)#
So:
#u = 4" "# or#" "u = -1#
Note that these are both valid solutions of the original equation, since they do not cause any denominator to be