# SOLUTION: Please help me solve this equation: {{{ 9x^2+40xy-25y^2 over 18x^2+17xy-15y^2 }}} this is reduce to lowest term

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 Question 641737: Please help me solve this equation: this is reduce to lowest termAnswer by DrBeeee(378)   (Show Source): You can put this solution on YOUR website!With these messy coefficients, I use the quadratic equation to find the roots. For the numerator we have a = 9 b = 40y c = -15y^2 Using (-b+/-sqrt(b^2-4ac))/2a, we obtain the roots of the numerator are (1) x = 5/9y, -5y which gives the factors of the numerator as (3) Num = 9(x-5/9y)(x+5y) or (4) Num = (9x-5y)(x+5y) Foil (4) to check that Num = 9x^2 +40xy -25y^2 as given. Do the same for the denominator, ie use the quadratic equation with a = 18 b = 17y c = -25y^2 which gives the roots (5) x = 5/9y, -3/2y which gives the factors of the denominator as (6) Den = 18(x-5/9y)(x+3/2y) which reduces to (7) Den = (9x-5y)(2x+3y) FOIL (7) to check that Den = 18x^2 +17xy -15y^2 as given. The given expression is (8) Num/Den = (4)/(7) = [(9x-5y)(x+5y)]/[(9x-5y)(2x+3y)] Simplifying (8) yields the answer (9) (x+5y)/(2x+3y)