Solve the equation: (2x+3)/(x-4)-(2x-8)/(2x+1)=1

By solving this equation we are trying to find the value of x. First we must combine the two fractions into one by finding the common denominator. The least common denominator in this case is (x-4)(2x+1), i.e. multiplying the denominators of the two fractions, as there's no common factor. The numerator of each fraction must also be multiplied by the denominator of the other fraction, so we get ((2x+3)(2x+1)-(2x-8)(x-4))/((x-4)(2x+1))=1

Now we will expand the brackets and simplify, which results in (2x²+24x-29)/(2x²-7x-4)=1. We can multiply both sides of the equal sign by (2x²-7x-4), giving us 2x²+24x-29=2x²-7x-4, but as 2x² is on both the left and right side these cancel out. Now we can move the -7x from the right side to the left side and change the sign, and the -29 from the left side to the right side and also change the sign of it, resulting in 24x+7x=-4+29, and therefore 31x=25. Dividing both sides by 31 we have now found the value of x.

x=25/31, which to 2 decimal places can be written as x=0.81.