What is (x/4) - (2x/x+2) = 1 ?

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Answer 1 · 2018-06-27T11:52:49

#x=5+sqrt 33 # or # x=5-sqrt33#

#x/4-(2x)/(x+2)=1#

#:.(x(x+2)-4(2x)=4(x+2))/(4(x+2))#

#"multiply both sides by"##4(x+2)#

#:.x(x+2)-4(2x)=4(x+2)#

#:.x^2+2x-8x=4x+8#

#:.x^2+2x-8x-4x-8=0#

#:.x^2-10x-8=0#

#"quadratic formula:-"#

#:.x=(-b+-sqrt (b^2-4ac))/(2a)#

#:.a=1,b=-10,c=-8#

#:.x=(-(-10)+-sqrt ((-10)^2-4(1)(-8)))/2#

#:.x=(10+- sqrt(132))/2#

#:.x=(10+- sqrt(33*2*2))/2#

#:.x=(10+- 2 sqrt(33))/2#

#:.x=5+- sqrt 33#

#:.x=5+ sqrt 33 or x=5- sqrt 33 #