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Question Number 131641 by liberty last updated on 07/Feb/21
What is f(x) if : 2f(x)−x f(((2x+3)/(x−2)))=3  when x≠ 2 ?
Whatisf(x)if:2f(x)xf(2x+3x2)=3whenx2?
Answered by EDWIN88 last updated on 07/Feb/21
(1) 2f(x)−x f(((2x+3)/(x−2)))= 3   replacing x by ((2x+3)/(x−2))  (2) 2f(((2x+3)/(x−2)))−(((2x+3)/(x−2)))f(x)= 3   then multiply by (2)eq (1) and by x eq(2)   ⇒4f(x)−2x f(((2x+3)/(x−2)))= 6  ⇒ 2x f(((2x+3)/(x−2)))−(((2x^2 +3x)/(x−2)))f(x)= 3x     ^(−−−−−−−−−−−−−−−−−−−−−−−−)  +  ⇒ (((4x−8−2x^2 −3x)/(x−2)))f(x)= 6+3x   f(x)= (((x−2)(3x+6))/(x−2x^2 −8)) = ((3(x^2 −4))/(−2x^2 +x−8))   f(x)= ((3(4−x^2 ))/(2x^2 −x+8))
(1)2f(x)xf(2x+3x2)=3replacingxby2x+3x2(2)2f(2x+3x2)(2x+3x2)f(x)=3thenmultiplyby(2)eq(1)andbyxeq(2)4f(x)2xf(2x+3x2)=62xf(2x+3x2)(2x2+3xx2)f(x)=3x+(4x82x23xx2)f(x)=6+3xf(x)=(x2)(3x+6)x2x28=3(x24)2x2+x8f(x)=3(4x2)2x2x+8

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