Question

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

Answer 1

7/(2 x+1)-(8 x)/(2 x-1) = -4
Multiply both sides by 2 x-1:
(7 (2 x-1))/(2 x+1)-8 x = -4 (2 x-1)
Expand out terms on both sides:
(14 x)/(2 x+1)-8 x-7/(2 x+1) = 4-8 x
Write the left hand side as a single fraction:
(-16 x^2+6 x-7)/(2 x+1) = 4-8 x
Multiply both sides by 2 x+1:
-16 x^2+6 x-7 = 4 (2 x+1)-8 x (2 x+1)
Expand out terms on the right hand side:
-16 x^2+6 x-7 = 4-16 x^2
Subtract (4-16 x^2) from both sides:
6 x-11 = 0
Add 11 to both sides:
6 x = 11
Divide both sides by 6:
x = 11/6

Answer 2

move the RHS to the LHS\[7/(2x+1)-8x/(2x-1)+4=0\]Combine terms and simplify\[\frac{-11+6 x}{(-1+2 x) (1+2 x)}= 0\]Solve the following for x\[-11+6 x=0\]\[x=\frac{11}{6} \]