How do you solve #1/(2x-1) - 1/(2x+1) = 1/40 #?
1 Answer
Feb 8, 2016
Explanation:
Get a common denominator on the left hand side of the equation.
#(2x+1)/((2x-1)(2x+1))-(2x-1)/((2x-1)(2x+1))=1/40#
Note that that the fractions can be combined and that the denominator is
#(2x+1-(2x-1))/(4x^2-1)=1/40#
#(2x+1-2x+1)/(4x^2-1)=1/40#
#2/(4x^2-1)=1/40#
Cross-multiply.
#80=4x^2-1#
#0=4x^2-81#
Factor this as a difference of squares.
#0=(2x+9)(2x-9)#
Now, set these both equal to
#2x+9=0" "=>" "x=-9/2#
#2x-9=0" "=>" "x=9/2#