# SOLUTION: Help would be great!! x-4/x-5 - 3/x+5 = 10/(x-5)(x+5)

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 Click here to see ALL problems on Polynomials-and-rational-expressions Question 105706: Help would be great!! x-4/x-5 - 3/x+5 = 10/(x-5)(x+5) Answer by ankor@dixie-net.com(15634)   (Show Source): You can put this solution on YOUR website!: - = : We can get rid of the denominators if we multiply thru by (x-5)(x+5) (x-5)(x+5)* - (x-5)(x+5)* = (x-5)(x+5)* : Cancel out the denominator and you have: (x+5)(x-4) - 3(x-5) = 10 : FOIL, then combine like terms on the left: (x^2 + x - 20) - 3x + 15 = 10 : x^2 + x - 3x - 20 + 15 - 10 = 0 : x^2 - 2x - 15 = 0: a quadratic equation, we can factor : (x-5)(x+3) = 0 : x = +5 and x = -3 : It's important to notice that x = +5 is NOT a solution, as it produces division by 0 in the original equation : The leaves us with a solution: x = -3 : Substituting -3 for x in the original equation: - = : - = : - = : - = -; confirms our solution : Was this helpful?