Solve the equation. startfraction 2 x plus 1 over x minus 2 endfraction plus startfraction 4 over x endfraction equals startfraction negative 8 over x squared minus 2 x endfraction select the correct choice below and, if necessary, fill in the answer box to complete your choice.

  x = -5/2

Given

(2x+1)/(x-2) + 4/x= -8/(x^2-2x)

Find

x

Solution

We note that the denominators in this equation are x and x-2. The solution set must exclude these values, as the equation is "undefined" for those values of x.

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Multiply by x(x-2)

  x(2x+1) +4(x-2) = -8

  2x² +5x = 0 . . . . . . . . . . add 8, eliminate parentheses

  x(2x +5) = 0

The solutions are the values of x that make these factors zero:

  x = 0 . . . . must be excluded

  x = -5/2

The solution to the equation is x = -5/2.