Solve 5x/(2x+1) - 3/(x+1) = 1

This is an algebraic fractional equation. Dealing with algebraic equations and adding/subtracting fractions is not too bad, so we'll need to think about both when looking at this questions.1) Firstly, we need to simplify the left hand side (LHS) because we can't deal with its current form. To do this we need to have a common denominator. The way we do this is the same as with adding numerical fractions. We multiply the top and bottom of each fraction by the denominator of the other to get 5x(x+1)/((2x+1)(x+1)) - 3(2x+1)/((2x+1)(x+1)) . Now they have the same denominator we can combine the numerators and remember that it's all equal to one to get 5x(x + 1) – 3(2x + 1)/((2x + 1)(x + 1)) = 1. Rearranging by multiplying both sides by the denominator gives us 5x(x + 1) – 3(2x + 1) = (2x + 1)(x + 1). This looks like an equation we can solve. 2) If we then expand the brackets on both sides and move everything to one side we get 3x^2 – 4x – 4 = 0. This is just a quadratic! 3) The easiest way to solve a quadratic is by factorising so we can try and we see it can be factorised to give (3x + 2)(x – 2) = 0. This has solutions x = −2/3 or 2. 4) The final step is to check with the original equation. We try this and of course find that if we plug in either of our answers then 1 pops out! Job done.