Solve for x

1/x+1/(x+16)=1/15

I think I finally got this one

x=24, x=-10
correct?

correct.

Just plug in the values of x to check if those value are correct!

To solve for x in the equation:

1/x + 1/(x + 16) = 1/15

We need to get rid of the denominators by finding a common denominator. In this case, the common denominator is 15x(x + 16).

Multiplying both sides of the equation by 15x(x + 16) will eliminate the fractions:

15(x + 16) + 15x = x(x + 16)

Expanding the brackets:

15x + 240 + 15x = x^2 + 16x

Combining like terms:

30x + 240 = x^2 + 16x

Rearranging the equation:

x^2 + 16x - 30x - 240 = 0

Simplifying:

x^2 - 14x - 240 = 0

Now, we can solve this quadratic equation. We can factor this equation or use the quadratic formula. Let's use the quadratic formula:

The quadratic formula is given by:

x = (-b ± √(b^2 - 4ac))/(2a)

For our equation, a = 1, b = -14, and c = -240. Substituting these values into the quadratic formula:

x = (14 ± √((-14)^2 - 4(1)(-240)))/(2(1))

Simplifying:

x = (14 ± √(196 + 960))/2

x = (14 ± √1156)/2

x = (14 ± 34)/2

Now, we have two possible solutions:

x1 = (14 + 34)/2 = 48/2 = 24
x2 = (14 - 34)/2 = -20/2 = -10

Hence, the solutions for x in the equation are x = 24 and x = -10.