3/x-5=10/x+2
is it 3/(x-5)
or 3/x -5?
if it is 3/(x-5)=10/(x+2)
then the answer is 8
cross multiply= 3x+6=10X-50
56=7x
x=8
To solve the equation 3/x - 5 = 10/x + 2, we can start by getting rid of the fractions. We can do this by multiplying every term in the equation by the common denominator, which is x(x+2).
Multiply every term by x(x+2):
(x(x+2))(3/x) - (x(x+2))(5) = (x(x+2))(10/x) + (x(x+2))(2)
Now let's simplify each term:
3(x+2) - 5x(x+2) = 10(x+2) + 2x(x+2)
Distribute and simplify:
3x + 6 - 5x^2 - 10x = 10x + 20 + 2x^2 + 4x
Combine like terms:
3x - 5x^2 - 10x = 10x + 20 + 2x^2 + 4x
Combine like terms again:
-5x^2 - 7x = 14x + 20
Rearrange all terms to one side of the equation:
-5x^2 - 7x - 14x - 20 = 0
Combine like terms:
-5x^2 - 21x - 20 = 0
Now, we have a quadratic equation. To solve it, we can either factor, complete the square, or use the quadratic formula. Factoring may not be straightforward for this equation, so let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For the equation -5x^2 - 21x - 20 = 0, we have a = -5, b = -21, and c = -20.
Plugging them into the quadratic formula:
x = (-(-21) ± √((-21)^2 - 4(-5)(-20))) / (2(-5))
Simplifying:
x = (21 ± √(441 - 400)) / (-10)
x = (21 ± √41) / (-10)
Thus, the solutions to the equation 3/x - 5 = 10/x + 2 are:
x = (21 + √41) / (-10)
x = (21 - √41) / (-10)