section+2.7

2.7 __Solving Rational Equations__ __Steps__: 1. Factor the denominators 2. Find the LCD 3. Multiply the LCD to remove all the fractions. 5. Check for extraneous solutions(apparent solutions that do not work in the original problem). __Ex.1__ x+3/x=4 x=LCD multiply each side by x x(x+3/x)=(4)x x^2+3=4x bring 4x to the other side x^2+4x+3=0 factor the equation (x-3)(x-1) set each to zero x-3=0, x-1=0 solve x=3, x=1 than make sure to plug in so the numbers dont make the denominator 0. __Ex.2__ 2x/x-1+1/x-3=2/x^2-4x+3 factor the quadratic to make it a polynomial 2x/x-1+1/x-3=2/(x-3)(x-1) LCD=(x-3)(x-1) multiply LCD (x-3)(x-1)(2x/x-1+1/x-3)=(x-3)(x-1)(2/(x-3)(x-1) cancel out terms 2x(x-3)=1(x-1)=2 2x^2-6x=x-1=2 add alike terms 2x^2-5x-3 (2x+1)(x-3)=0 make each term equal to zero (2x-1)=0, x-3=0 x=-1/2, x=3 test to see if any of the answers make the equation equal 0.