Solve for x 7/(2x+1)-(8x)/(2x-1)=-4

Problem

7/(2*x+1)−(8*x)/(2*x−1)=−4

Solution

1. Identify the common denominator by multiplying the two denominators on the left side, which is (2*x+1)*(2*x−1)

2. Multiply every term in the equation by the common denominator (2*x+1)*(2*x−1) to eliminate the fractions.

7*(2*x−1)−8*x*(2*x+1)=−4*(2*x+1)*(2*x−1)

3. Expand the expressions on both sides of the equation.

14*x−7−16*x2−8*x=−4*(4*x2−1)

4. Simplify the left side by combining like terms.

−16*x2+6*x−7=−4*(4*x2−1)

5. Distribute the constant on the right side.

−16*x2+6*x−7=−16*x2+4

6. Add 16*x2 to both sides to eliminate the quadratic terms.

6*x−7=4

7. Isolate the variable by adding 7 to both sides and then dividing by 6.

6*x=11

x=11/6

Final Answer

7/(2*x+1)−(8*x)/(2*x−1)=−4⇒x=11/6

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