How do you solve #\frac { x ^ { 2} - x - 6} { x ^ { 2} } - \frac { 2x + 12} { x } = \frac { x - 6} { 2x }#?

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Answer 1 · 2017-09-10T11:32:44

Solution: #x= -6 , x = -2/3#

#(x^2-x-6)/x^2 - (2x+12)/x = (x-6)/(2x)#

Multiplying by #2x^2# on both sides we get,

#2(x^2-x-6) -2x (2x+12) = x(x-6) # or

#2x^2-2x-12 -4x^2-24x - x^2+6x = 0 # or

#-3x^2-20x-12=0 or 3x^2+20x = -12# or

# 3(x^2 +20/3x) = -12 # or

Adding #100/3# on both sides we get,

#3{x^2+20/3x +(10/3)^2}= -12 +100/3# or

# 3 ( x+10/3)^2=64/3 or ( x+10/3)^2=64/9 #or

# ( x+10/3)=+-sqrt(64/9) or x= -10/3+- 8/3 # or

#x= -6 , x = -2/3# [Ans]