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

Question 641737: Please help me solve this equation:
this is reduce to lowest term
Answer by DrBeeee(684) (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)
RELATED QUESTIONS
Need help with this factoring equation: 3x^2-17xy+24y^2 My try:9x-17xy+576y... (answered by jim_thompson5910,solver91311)

Please help me solve this equation... (answered by Boreal,MathLover1)

Please help me solve this equation:... (answered by mananth)

Please help. Factor the trinomial. 16x^2 + 40xy +... (answered by jim_thompson5910)

factor this trinomial 16x^2 + 40xy +... (answered by gsmani_iyer)

Please help... Reduce the expression to the lowest term: 5a-10b over 4b^2 - a^2 (answered by MathLover1)

16x^2 + 40xy +... (answered by ReadingBoosters)

Please help me solve this equation ((( -5y^4(y^5)^2 over... (answered by Theo)

Can you please help me solve this equation:... (answered by stanbon)