How do you solve #x /( 2x + 1 ) + ( 1 / 4 ) = 2 / (2x + 1)# and find any extraneous solutions?
2 Answers
Solution:
Explanation:
both sides we get ,
Check: L.H.S
R.H.S
L.H.S=R.H.S , no extraneous root.
Solution:
Explanation:
#"since fractions on both sides of the equation have a"#
#color(blue)"common denominator "" we can combine them"#
#"subtract "2/(2x+1)" from both sides"#
#x/(2x+1)-2/(2x+1)+1/4=0#
#"subtract "1/4" from both sides"#
#x/(2x+1)-2/(2x+1)cancel(+1/4)cancel(-1/4)=0-1/4#
#rArr(x-2)/(2x+1)=-1/4larrcolor(blue)"combining fractions"#
#"using the method of "color(blue)"cross-multiplying"#
#•color(white)(x)a/b=c/drArraxxd=bxxc#
#"attaching the negative sign to 1 "#
#rArr-1(2x+1)=4(x-2)#
#rArr-2x-1=4x-8larrcolor(blue)"distributing"#
#"subtract 4x from both sides"#
#-2x-4x-1=cancel(4x)cancel(-4x)-8#
#rArr-6x-1=-8#
#"add 1 to both sides"#
#-6xcancel(-1)cancel(+1)=-8+1#
#rArr-6x=-7#
#"divide both sides by "-6#
#(cancel(-6) x)/cancel(-6)=(-7)/(-6)#
#rArrx=7/6" is the solution"#
#"there are no extraneous solutions"#