trying to solve a fraction using variables

[Failenn]

i have to solve this problem

6/x + 8/(x +5) = 10. First I found the common denominator and multiplied it through.

x(x+5)(6/x) + x(x+5)(8/(x+5)) = x(x+5)(10) then I did some crossing out to give me...

6(x+5) + 8(x) = 10(x^2 + 5x) solving...
6x + 30 +8x = 10x^2 + 50x
14x + 30 = 10x^2 + 50x
0 = 10x^2 + 50x - 14x - 30
0= 10x^2 + 36x - 30.

From what I can see, you can't solve it to get a "foil" method so I have to use the quadriatic equation.....

-36 +/- sqrt[(36)^2 - (4 * 10 * -30)]
2(10)

-36 +/- sqrt[1296 + 1200]
20

-36 +/- sqrt[1496]
20

-36 +/- 2sqrt[374]
20

-18 +/- sqrt[374]
10

for some reason it just doesn't seem correct and trying to double check to see if both work in orginal equation, I got stumped in how to solve. the complex fraction combined with the sqrt has me just a bit confused.

 

[Deleted member 4993]

i have to solve this problem

6/x + 8/(x +5) = 10. First I found the common denominator and multiplied it through.

x(x+5)(6/x) + x(x+5)(8/(x+5)) = x(x+5)(10) then I did some crossing out to give me...

6(x+5) + 8(x) = 10(x^2 + 5x) solving...
6x + 30 +8x = 10x^2 + 50x
14x + 30 = 10x^2 + 50x
0 = 10x^2 + 50x - 14x - 30
0= 10x^2 + 36x - 30.

From what I can see, you can't solve it to get a "foil" method so I have to use the quadriatic equation.....

-36 +/- sqrt[(36)^2 - (4 * 10 * -30)]
2(10)

-36 +/- sqrt[1296 + 1200]
20

-36 +/- sqrt[1496]? 1296 + 1200 = 2496 - otherwise work is correct
20

-36 +/- 2sqrt[374]
20

-18 +/- sqrt[374]
10

for some reason it just doesn't seem correct and trying to double check to see if both work in orginal equation, I got stumped in how to solve. the complex fraction combined with the sqrt has me just a bit confused.

 

[Failenn]

Thank you.

I'm working on a review which my teacher gave us so we have an idea of what to expect for the final. And some of the problems I've been a bit lost on, and not remembering some things.

 

[Denis]

0= 10x^2 + 36x - 30.
From what I can see, you can't solve it to get a "foil" method so I have to use the quadriatic equation.....

Make your life simpler by reducing as much as possible; here, you can divide by 2:
5x^2 + 18x - 15 = 0
Now call in the quadratic!