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solve-5-3x-2-8-4x-2-33-9x-8-




Question Number 8350 by Nayon last updated on 09/Oct/16
solve:           (5/(3x+2))+(8/(4x+2))=((33)/(9x+8))
$${solve}: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\frac{\mathrm{5}}{\mathrm{3}{x}+\mathrm{2}}+\frac{\mathrm{8}}{\mathrm{4}{x}+\mathrm{2}}=\frac{\mathrm{33}}{\mathrm{9}{x}+\mathrm{8}} \\ $$
Answered by Rasheed Soomro last updated on 10/Oct/16
 (5/(3x+2))+(8/(4x+2))=((33)/(9x+8))  Multiplying both sides by (3x+2)(4x+2)(9x+8)  5(4x+2)(9x+8)+8(3x+2)(9x+8)=33(3x+2)(4x+2)  5(36x^2 +50x+16)+8(27x^2 +42x+16)                                                 =33(12x^2 +14x+4)  180x^2 +250x+80+216x^2 +336x+128−396x^2 −462x−132=0  124x+76=0  x=−((76)/(124))=((19)/(31))
$$\:\frac{\mathrm{5}}{\mathrm{3}{x}+\mathrm{2}}+\frac{\mathrm{8}}{\mathrm{4}{x}+\mathrm{2}}=\frac{\mathrm{33}}{\mathrm{9}{x}+\mathrm{8}} \\ $$$$\mathrm{Multiplying}\:\mathrm{both}\:\mathrm{sides}\:\mathrm{by}\:\left(\mathrm{3}{x}+\mathrm{2}\right)\left(\mathrm{4}{x}+\mathrm{2}\right)\left(\mathrm{9}{x}+\mathrm{8}\right) \\ $$$$\mathrm{5}\left(\mathrm{4}{x}+\mathrm{2}\right)\left(\mathrm{9}{x}+\mathrm{8}\right)+\mathrm{8}\left(\mathrm{3}{x}+\mathrm{2}\right)\left(\mathrm{9}{x}+\mathrm{8}\right)=\mathrm{33}\left(\mathrm{3}{x}+\mathrm{2}\right)\left(\mathrm{4}{x}+\mathrm{2}\right) \\ $$$$\mathrm{5}\left(\mathrm{36x}^{\mathrm{2}} +\mathrm{50x}+\mathrm{16}\right)+\mathrm{8}\left(\mathrm{27x}^{\mathrm{2}} +\mathrm{42x}+\mathrm{16}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{33}\left(\mathrm{12x}^{\mathrm{2}} +\mathrm{14x}+\mathrm{4}\right) \\ $$$$\mathrm{180x}^{\mathrm{2}} +\mathrm{250x}+\mathrm{80}+\mathrm{216x}^{\mathrm{2}} +\mathrm{336x}+\mathrm{128}−\mathrm{396x}^{\mathrm{2}} −\mathrm{462x}−\mathrm{132}=\mathrm{0} \\ $$$$\mathrm{124x}+\mathrm{76}=\mathrm{0} \\ $$$$\mathrm{x}=−\frac{\mathrm{76}}{\mathrm{124}}=\frac{\mathrm{19}}{\mathrm{31}} \\ $$

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