Solve for x: |
\[\frac{2}{x+1}+\frac{3}{2(x-2)}=\frac{23}{5x},x\ne 0,-1,2\] |
Answer:
We have, \[\frac{2}{x+1}+\frac{3}{2(x-2)}=\frac{23}{5x},x\ne 0,-1,2\] \[\Rightarrow 2(10x)(x-2)+3(5x)(x+1)=23(2)(x+1)(x-2)\] \[\Rightarrow 20x(x-2)+15x(x+1)=46(x+1)(x-2)\] \[\Rightarrow 20{{x}^{2}}-40x+15{{x}^{2}}+15x=46({{x}^{2}}+x-2x-2)\] \[\Rightarrow 20{{x}^{2}}-40x+15{{x}^{2}}+15x=46{{x}^{2}}-46x-92\] \[\Rightarrow 11{{x}^{2}}-21x-92=0\] \[\Rightarrow x=\frac{21\pm \sqrt{441+4048}}{22}\] \[\Rightarrow x=\frac{21\pm \sqrt{4489}}{22}\] \[\Rightarrow x=\frac{21\pm 67}{22}\] \[\Rightarrow x=\frac{21+67}{22}or\,\frac{21-67}{22}\] \[\Rightarrow x=\frac{88}{22}or-\,\frac{46}{22}\] \[\therefore x=4\] or \[-\frac{23}{11}\]
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