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Question

Solve for x: 1x+1+35x+1=5x+4,x1,15,4

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Solution

Given, 1x+1+35x+1=5x+41x+15x+4=35x+1(x+4)5(x+1)(x+1)(x+4)=35x+1x+45x5x2+5x+4=35x+1(4x1)x2+5x+4=35x+1(4x+1)(5x+1)=3(x2+5x+4)20x2+4x+5x+1=3x2+15x+1217x26x11=017x217x+11x11=017x(x1)+11(x1)=0(x1)(17x+11)=0Either x=1 or x=1117

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