SOLUTION: Find all real solutions of the equation. x divided by 2x+6 minus x-9 divided x+5 = 1 x = ____ (smaller value) x = ____(larger value)

Algebra ->  Pythagorean-theorem -> SOLUTION: Find all real solutions of the equation. x divided by 2x+6 minus x-9 divided x+5 = 1 x = ____ (smaller value) x = ____(larger value)       Log On


   

Question 178970: Find all real solutions of the equation.
x divided by 2x+6 minus x-9 divided x+5 = 1
x = ____ (smaller value)
x = ____(larger value)
Found 2 solutions by stanbon, solver91311:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
x divided by 2x+6 minus x-9 divided x+5 = 1
x = ____ (smaller value)
x = ____(larger value)
----------------------
[x/(2x+6)] - [(x-9)/(x+5)] = 1
Multiply thru by (2x+6)(x+5) to get:
x(x+5) - (2x+6)(x-9) = (x+5)(2x+6)
x^2 + 5x -[2x^2 - 12x - 54] = 2x^2 + 16x + 30
-x^2 + 17x + 54 = 2x^2 + 16x + 30
3x^2 -x - 24 = 0
3x^2 - 9x + 8x - 24 = 0
3x(x-3) + 8(x-3) = 0
(x-3)(3x+8) = 0
x = 3 or x = -8/3
------------------------------------
Cheers,
Stan H.

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!




First find the Lowest Common Denominator. Since the two denominators have no factors in common, the LCD is simply the product of the two denominators.



We can simplify this horror by realizing that since the denominators are now equal, we only have to concern ourselves with the sum of the numerators on the left being equal to the numerator on the right. This is because:



So, we can write:



Apply the distributive property and FOIL twice:





Collect like terms and put the equation in standard form for a quadratic:



This actually factors:

So or