Simplify fully the following equation: X^2-2x-15/2x^2-9x-5

We first need to simplify both the numerator and denominator of this fraction seperately. Let's start with the numerator: x^2 -2x -15We need to find two numbers that add to make -2 and multiply to make -15. That would be -5 and +3. We then put these numbers into our two brackets: (x-5)(x+3). This would multiply out to give us x^2-2x-15Next let's take the denominator:2x^2-9x-5This time we need two numbers that add to give -9 and multiply to give -10 (2 x -5). That would be -10 and +1Let's write this out: 2x^2 - 10x +1x -5. The equation hasn't changed, we've just added another step in to help us simplify it now.2x is a factor of the first two elements of this equation, so we can take that out and rewrite it as:2x(x-5) +1x -5 We can now see that (x-5) is also a factor of that second section so we can rewrite that as: 2x(x-5) +1(x-5) Now we've found one of the brackets we can simplify the whole of the denominator to: (2x+1)(x-5) So our whole fraction now looks like this: (x-5)(x+3)/(2x+1)(x-5)Now we can cancel out the (x-5) because it appears in both the numerator and denominator, so the simplified equation is:(x+3)/(2x+1)