Question

How do i solve this?

Answer 1

The answer is x^2 - 4x +4. What I did was set it up as a ratio, FOILing out the two denominators on the left to get (x-5)?/(x^2 - 7x + 10) = (x+1)/1. Next I cross-multiplied to get (x-5)? = (x+1)(x^2 - 7x + 10). Next I FOILed out the right side to get (x-5)? = x^3 - 9x^2 + 24x - 20.  Now I have an equation just like 3x=9, for example, where I divide both sides by 3 to find x. Instead, since we have polynomials, we have to use long division. Divide the x^3 term by x-5 and you'll get it.