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"