solve -5x/3x+3 = 2x/6x+6 + 6x-4/x+1

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Multiply through by x+1 (assuming x≠-1):

-5x/3=x/3+6x-4 [NOTE: 3x+3=3(x+1) and 2x/(6x+6)=x/(3x+3); and 5x/3+x/3=(5+1)x/3=6x/3=2x],

4=5x/3+x/3+6x=8x, x=4/8=½. This also satisfies the assumption that x is not equal to -1.

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