Find the solution set.
x/x-2 - 5/x = 3/4
2007-05-17 05:36:44 · 3 answers · asked by spoons 1 in Science & Mathematics ➔ Mathematics
x/x-2 - 5/x = 3/4
Multiply by denominators to get rid of them
First by 4
4x/x-2 -20/x = 3
Next by x
4x^2/x-2 - 20 = 3x
Now by x-2
4x^2 -20(x-2) =3x(x-2)
Simplify
4x^2-20x+40 = 3x^2-6x
Again
x^2-14x+40 = 0
Factor
(x-10)(x-4)=0
x = 10, 4
2007-05-17 05:42:18 · answer #1 · answered by ignoramus 7 · 0⤊ 0⤋
Multiply by the LCD of 4x(x-2) and clear the equation of fractions.
You get 4x(x) - 4(x-2)5 =x(x-2)3
Simplify
4x^2 -20x+40 = 3x^2-6x
Set the equation = to 0
x^2 -14x +40 = 0
Factor
(x-4)(x-10) = 0
x = 4 and x = 10
Check the answers and they both check.
2007-05-17 05:46:25 · answer #2 · answered by lizzie 3 · 0⤊ 0⤋
x / (x - 2) - 5 / x = 3 / 4
4x² - 20.(x - 2) = 3x.(x - 2)
4x² - 20x + 40 = 3x² - 6x
x² - 14x + 40 = 0
(x - 10).(x - 4) = 0
x = 4, x = 10
2007-05-17 09:06:48 · answer #3 · answered by Como 7 · 0⤊ 0⤋