How do you solve #\frac { x + 6} { 2} + \frac { 3} { x } = \frac { 1} { 2x }#?

2 Answers
Mark D.
May 22, 2018

#x=-5 or -1#

Explanation:

Multiply everything by #2x# and this will remove the fractions.

#2x xx(x+6)/2+2x xx3/x=2x xx1/(2x)#

#x^2+6x+6=1#

#x^2+6x+5=0#

#(x+5)(x+1)=0#

#x=-5 or -1#

Jim G.
May 22, 2018

#x=-5" or "x=-1#

Explanation:

#"multiply through by the "color(blue)"lowest common multiple"#
#"of the values on the denominators"#

#"the lowest common multiple of 2 ," x" and "2x" is "2x#

#cancel(2)x xx(x+6)/cancel(2)+2cancel(x)xx3/cancel(x)=cancel(2x)xx1/cancel(2x)#

#rArrx(x+6)+6=1#

#rArrx^2+6x+6=1#

#"subtract 1 from both sides"#

#rArrx^2+6x+5=0larrcolor(blue)"in standard form"#

#"the factors of + 5 which sum to + 6 are + 5 and + 1"#

#rArr(x+5)(x+1)=0#

#"equate each factor to zero and solve for x"#

#x+5=0rArrx=-5#

#x+1=0rArrx=-1#

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